diff --git a/libraries/tools/kotlin-gradle-plugin-integration-tests/src/test/kotlin/org/jetbrains/kotlin/gradle/AppleFrameworkIT.kt b/libraries/tools/kotlin-gradle-plugin-integration-tests/src/test/kotlin/org/jetbrains/kotlin/gradle/AppleFrameworkIT.kt
index 5733df61bd7..7edcc06d05c 100644
--- a/libraries/tools/kotlin-gradle-plugin-integration-tests/src/test/kotlin/org/jetbrains/kotlin/gradle/AppleFrameworkIT.kt
+++ b/libraries/tools/kotlin-gradle-plugin-integration-tests/src/test/kotlin/org/jetbrains/kotlin/gradle/AppleFrameworkIT.kt
@@ -5,15 +5,15 @@
 
 package org.jetbrains.kotlin.gradle
 
+import org.jetbrains.kotlin.gradle.util.AGPVersion
 import org.jetbrains.kotlin.konan.target.HostManager
+import org.jetbrains.kotlin.test.util.KtTestUtil
 import org.junit.Assume
 import org.junit.BeforeClass
 import kotlin.test.Test
 
-class AppleFrameworkIT : KotlinAndroid36GradleIT() {
+class AppleFrameworkIT : BaseGradleIT() {
     companion object {
-        private val gradleVersion = GradleVersionRequired.FOR_MPP_SUPPORT
-
         @BeforeClass
         @JvmStatic
         fun assumeItsMac() {
@@ -21,11 +21,14 @@ class AppleFrameworkIT : KotlinAndroid36GradleIT() {
         }
     }
 
-    override val defaultGradleVersion: GradleVersionRequired
-        get() = gradleVersion
+    override val defaultGradleVersion = GradleVersionRequired.FOR_MPP_SUPPORT
+    override fun defaultBuildOptions() = super.defaultBuildOptions().copy(
+        androidHome = KtTestUtil.findAndroidSdk(),
+        androidGradlePluginVersion = AGPVersion.v3_6_0
+    )
 
     @Test
-    fun `assemble debug AppleFrameworkForXcode for IosArm64`() {
+    fun `assemble AppleFrameworkForXcode tasks for IosArm64`() {
         with(Project("sharedAppleFramework")) {
             val options: BuildOptions = defaultBuildOptions().copy(
                 customEnvironmentVariables = mapOf(
@@ -33,18 +36,18 @@ class AppleFrameworkIT : KotlinAndroid36GradleIT() {
                     "SDK_NAME" to "iphoneos123"
                 )
             )
-            build("assembleSharedDebugAppleFrameworkForXcodeIosArm64", options = options) {
+            build("assembleDebugAppleFrameworkForXcodeIosArm64", options = options) {
                 assertSuccessful()
-                assertTasksExecuted(":shared:assembleSharedDebugAppleFrameworkForXcodeIosArm64")
-                assertFileExists("/shared/build/xcode-frameworks/debug/iphoneos123/shared.framework")
-                assertFileExists("/shared/build/xcode-frameworks/debug/iphoneos123/shared.framework.dSYM")
+                assertTasksExecuted(":shared:assembleDebugAppleFrameworkForXcodeIosArm64")
+                assertFileExists("/shared/build/xcode-frameworks/debug/iphoneos123/sdk.framework")
+                assertFileExists("/shared/build/xcode-frameworks/debug/iphoneos123/sdk.framework.dSYM")
             }
 
-            build("assembleSharedDebugAppleFrameworkForXcodeIosArm64", options = options) {
+            build("assembleCustomDebugAppleFrameworkForXcodeIosArm64", options = options) {
                 assertSuccessful()
-                assertTasksUpToDate(":shared:assembleSharedDebugAppleFrameworkForXcodeIosArm64")
-                assertFileExists("/shared/build/xcode-frameworks/debug/iphoneos123/shared.framework")
-                assertFileExists("/shared/build/xcode-frameworks/debug/iphoneos123/shared.framework.dSYM")
+                assertTasksExecuted(":shared:assembleCustomDebugAppleFrameworkForXcodeIosArm64")
+                assertFileExists("/shared/build/xcode-frameworks/debug/iphoneos123/lib.framework")
+                assertFileExists("/shared/build/xcode-frameworks/debug/iphoneos123/lib.framework.dSYM")
             }
         }
     }
@@ -55,8 +58,8 @@ class AppleFrameworkIT : KotlinAndroid36GradleIT() {
             build("tasks") {
                 assertSuccessful()
                 assertTasksNotRegistered(
-                    ":shared:assembleSharedDebugAppleFrameworkForXcodeIosArm64",
-                    ":shared:embedAndSignSharedAppleFrameworkForXcode"
+                    ":shared:assembleDebugAppleFrameworkForXcodeIosArm64",
+                    ":shared:embedAndSignAppleFrameworkForXcode"
                 )
             }
         }
@@ -77,10 +80,19 @@ class AppleFrameworkIT : KotlinAndroid36GradleIT() {
             build("tasks", options = options) {
                 assertSuccessful()
                 assertTasksRegistered(
-                    ":shared:assembleSharedDebugAppleFrameworkForXcodeIosArm64",
-                    ":shared:embedAndSignSharedAppleFrameworkForXcode"
+                    ":shared:assembleDebugAppleFrameworkForXcodeIosArm64",
+                    ":shared:embedAndSignAppleFrameworkForXcode",
+                    ":shared:assembleCustomDebugAppleFrameworkForXcodeIosArm64",
+                    ":shared:embedAndSignCustomAppleFrameworkForXcode"
+                )
+                assertTasksNotRegistered(
+                    ":shared:assembleDebugAppleFrameworkForXcodeIosX64",
+                    ":shared:assembleReleaseAppleFrameworkForXcodeIosX64",
+                    ":shared:assembleReleaseAppleFrameworkForXcodeIosArm64",
+                    ":shared:assembleCustomDebugAppleFrameworkForXcodeIosX64",
+                    ":shared:assembleCustomReleaseAppleFrameworkForXcodeIosX64",
+                    ":shared:assembleCustomReleaseAppleFrameworkForXcodeIosArm64"
                 )
-                assertTasksNotRegistered(":shared:assembleSharedDebugAppleFrameworkForXcodeIosX64")
             }
         }
     }
@@ -97,11 +109,14 @@ class AppleFrameworkIT : KotlinAndroid36GradleIT() {
             build("tasks", options = options) {
                 assertSuccessful()
                 assertTasksRegistered(
-                    ":shared:assembleSharedDebugAppleFrameworkForXcodeIosArm64",
+                    ":shared:assembleDebugAppleFrameworkForXcodeIosArm64",
+                    ":shared:assembleCustomDebugAppleFrameworkForXcodeIosArm64"
                 )
                 assertTasksNotRegistered(
-                    ":shared:embedAndSignSharedAppleFrameworkForXcode",
-                    ":shared:assembleSharedDebugAppleFrameworkForXcodeIosX64"
+                    ":shared:embedAndSignAppleFrameworkForXcode",
+                    ":shared:assembleDebugAppleFrameworkForXcodeIosX64",
+                    ":shared:embedAndSignCustomAppleFrameworkForXcode",
+                    ":shared:assembleCustomDebugAppleFrameworkForXcodeIosX64"
                 )
             }
         }
diff --git a/libraries/tools/kotlin-gradle-plugin-integration-tests/src/test/resources/testProject/sharedAppleFramework/shared/build.gradle.kts b/libraries/tools/kotlin-gradle-plugin-integration-tests/src/test/resources/testProject/sharedAppleFramework/shared/build.gradle.kts
index 726353469ba..832d659b34e 100644
--- a/libraries/tools/kotlin-gradle-plugin-integration-tests/src/test/resources/testProject/sharedAppleFramework/shared/build.gradle.kts
+++ b/libraries/tools/kotlin-gradle-plugin-integration-tests/src/test/resources/testProject/sharedAppleFramework/shared/build.gradle.kts
@@ -9,7 +9,10 @@ kotlin {
     ios() {
         binaries {
             framework {
-                baseName = "shared"
+                baseName = "sdk"
+            }
+            framework("custom") {
+                baseName = "lib"
             }
         }
     }
diff --git a/libraries/tools/kotlin-gradle-plugin/src/main/kotlin/org/jetbrains/kotlin/gradle/dsl/KotlinNativeBinaryContainer.kt b/libraries/tools/kotlin-gradle-plugin/src/main/kotlin/org/jetbrains/kotlin/gradle/dsl/KotlinNativeBinaryContainer.kt
index b509027150a..0f405c14bb8 100644
--- a/libraries/tools/kotlin-gradle-plugin/src/main/kotlin/org/jetbrains/kotlin/gradle/dsl/KotlinNativeBinaryContainer.kt
+++ b/libraries/tools/kotlin-gradle-plugin/src/main/kotlin/org/jetbrains/kotlin/gradle/dsl/KotlinNativeBinaryContainer.kt
@@ -160,6 +160,14 @@ open class KotlinNativeBinaryContainer @Inject constructor(
         internal fun generateBinaryName(prefix: String, buildType: NativeBuildType, outputKindClassifier: String) =
             lowerCamelCaseName(prefix, buildType.getName(), outputKindClassifier)
 
+        internal fun extractPrefixFromBinaryName(name: String, buildType: NativeBuildType, outputKindClassifier: String): String {
+            val suffix = lowerCamelCaseName(buildType.getName(), outputKindClassifier)
+            return if (name == suffix)
+                ""
+            else
+                name.substringBeforeLast(suffix.capitalize())
+        }
+
         // TODO: Remove in 1.3.50.
         private val GET_TEST_DEPRECATION_WARNING = """
             |
diff --git a/libraries/tools/kotlin-gradle-plugin/src/main/kotlin/org/jetbrains/kotlin/gradle/plugin/mpp/apple/AppleXcodeTasks.kt b/libraries/tools/kotlin-gradle-plugin/src/main/kotlin/org/jetbrains/kotlin/gradle/plugin/mpp/apple/AppleXcodeTasks.kt
index 9c63b92ae66..55c9824cef0 100644
--- a/libraries/tools/kotlin-gradle-plugin/src/main/kotlin/org/jetbrains/kotlin/gradle/plugin/mpp/apple/AppleXcodeTasks.kt
+++ b/libraries/tools/kotlin-gradle-plugin/src/main/kotlin/org/jetbrains/kotlin/gradle/plugin/mpp/apple/AppleXcodeTasks.kt
@@ -9,6 +9,7 @@ import org.gradle.api.Project
 import org.gradle.api.plugins.BasePlugin
 import org.gradle.api.tasks.Copy
 import org.gradle.api.tasks.TaskProvider
+import org.jetbrains.kotlin.gradle.dsl.KotlinNativeBinaryContainer
 import org.jetbrains.kotlin.gradle.plugin.mpp.Framework
 import org.jetbrains.kotlin.gradle.plugin.mpp.NativeBuildType
 import org.jetbrains.kotlin.gradle.plugin.mpp.enabledOnCurrentHost
@@ -73,8 +74,8 @@ private fun Project.registerAssembleAppleFrameworkTask(framework: Framework): Ta
     val frameworkTarget = framework.target
     val frameworkTaskName = lowerCamelCaseName(
         "assemble",
-        framework.baseName,
-        frameworkBuildType.name.toLowerCaseAsciiOnly(),
+        framework.namePrefix,
+        frameworkBuildType.getName(),
         "AppleFrameworkForXcode",
         frameworkTarget.name
     )
@@ -119,7 +120,7 @@ internal fun Project.registerEmbedAndSignAppleFrameworkTask(framework: Framework
     val envFrameworkSearchDir = XcodeEnvironment.frameworkSearchDir
     val envSign = XcodeEnvironment.sign
 
-    val frameworkTaskName = lowerCamelCaseName("embedAndSign", framework.baseName, "AppleFrameworkForXcode")
+    val frameworkTaskName = lowerCamelCaseName("embedAndSign", framework.namePrefix, "AppleFrameworkForXcode")
 
     if (envBuildType == null || envTarget == null || envEmbeddedFrameworksDir == null || envFrameworkSearchDir == null) {
         logger.debug(
@@ -133,7 +134,7 @@ internal fun Project.registerEmbedAndSignAppleFrameworkTask(framework: Framework
 
     registerTask<Copy>(frameworkTaskName) { task ->
         task.group = "build"
-        task.description = "Embed and sign ${framework.baseName} framework as requested by Xcode's environment variables"
+        task.description = "Embed and sign ${framework.namePrefix} framework as requested by Xcode's environment variables"
 
         task.dependsOn(assembleTask)
         task.inputs.apply {
@@ -162,5 +163,12 @@ internal fun Project.registerEmbedAndSignAppleFrameworkTask(framework: Framework
     }
 }
 
+private val Framework.namePrefix: String
+    get() = KotlinNativeBinaryContainer.extractPrefixFromBinaryName(
+        name,
+        buildType,
+        outputKind.taskNameClassifier
+    )
+
 private fun Project.appleFrameworkDir(frameworkSearchDir: File) =
     buildDir.resolve("xcode-frameworks").resolve(frameworkSearchDir)
\ No newline at end of file