diff --git a/platformio/package/commands/install.py b/platformio/package/commands/install.py
index 248a0b40..23589a5c 100644
--- a/platformio/package/commands/install.py
+++ b/platformio/package/commands/install.py
@@ -199,30 +199,49 @@ def _install_project_env_custom_tools(project_env, options):
 def _install_project_env_libraries(project_env, options):
     already_up_to_date = not options.get("force")
     config = ProjectConfig.get_instance()
-    lm = LibraryPackageManager(
+    env_lm = LibraryPackageManager(
         os.path.join(config.get("platformio", "libdeps_dir"), project_env)
     )
+    private_lm = LibraryPackageManager(
+        os.path.join(config.get("platformio", "lib_dir"))
+    )
     if options.get("silent"):
-        lm.set_log_level(logging.WARN)
+        env_lm.set_log_level(logging.WARN)
+        private_lm.set_log_level(logging.WARN)
     for library in config.get(f"env:{project_env}", "lib_deps"):
         spec = PackageSpec(library)
         # skip built-in dependencies
         if not spec.external and not spec.owner:
             continue
-        if not lm.get_package(spec):
+        if not env_lm.get_package(spec):
             already_up_to_date = False
-        lm.install(
+        env_lm.install(
             spec,
             skip_dependencies=options.get("skip_dependencies"),
             force=options.get("force"),
         )
     # install dependencies from the priate libraries
-    plm = LibraryPackageManager(os.path.join(config.get("platformio", "lib_dir")))
-    for pkg in plm.get_installed():
-        lm.install_dependencies(pkg, print_header=False)
+    for pkg in private_lm.get_installed():
+        _install_project_private_library_deps(pkg, private_lm, env_lm, options)
     return not already_up_to_date
 
 
+def _install_project_private_library_deps(private_pkg, private_lm, env_lm, options):
+    for dependency in private_lm.get_pkg_dependencies(private_pkg) or []:
+        spec = private_lm.dependency_to_spec(dependency)
+        # skip built-in dependencies
+        if not spec.external and not spec.owner:
+            continue
+        pkg = private_lm.get_package(spec)
+        if not pkg and not env_lm.get_package(spec):
+            pkg = env_lm.install(
+                spec,
+                skip_dependencies=True,
+                force=options.get("force"),
+            )
+        _install_project_private_library_deps(pkg, private_lm, env_lm, options)
+
+
 def _install_project_env_custom_libraries(project_env, options):
     already_up_to_date = not options.get("force")
     config = ProjectConfig.get_instance()
diff --git a/platformio/package/manager/_install.py b/platformio/package/manager/_install.py
index 24846be1..cd715e23 100644
--- a/platformio/package/manager/_install.py
+++ b/platformio/package/manager/_install.py
@@ -117,7 +117,7 @@ class PackageManagerInstallMixin(object):
 
     def install_dependencies(self, pkg, print_header=True):
         assert isinstance(pkg, PackageItem)
-        dependencies = dependencies = self.get_pkg_dependencies(pkg)
+        dependencies = self.get_pkg_dependencies(pkg)
         if not dependencies:
             return
         if print_header:
diff --git a/tests/commands/pkg/test_install.py b/tests/commands/pkg/test_install.py
index 3a2a1af8..d99e8f0d 100644
--- a/tests/commands/pkg/test_install.py
+++ b/tests/commands/pkg/test_install.py
@@ -219,22 +219,37 @@ platform = native
 """
     )
     with fs.cd(str(project_dir)):
+        config = ProjectConfig()
+
+        # some deps were added by user manually
+        result = clirunner.invoke(
+            package_install_cmd,
+            [
+                "-g",
+                "--storage-dir",
+                config.get("platformio", "lib_dir"),
+                "-l",
+                "paulstoffregen/OneWire@^2.3.5",
+            ],
+        )
+        validate_cliresult(result)
+
+        # ensure all deps are installed
         result = clirunner.invoke(package_install_cmd)
         validate_cliresult(result)
-        config = ProjectConfig()
-        installed_lib_pkgs = LibraryPackageManager(
-            os.path.join(config.get("platformio", "lib_dir"))
+        installed_private_pkgs = LibraryPackageManager(
+            config.get("platformio", "lib_dir")
         ).get_installed()
-        assert pkgs_to_specs(installed_lib_pkgs) == [
-            PackageSpec("My Private Lib@1.0.0")
+        assert pkgs_to_specs(installed_private_pkgs) == [
+            PackageSpec("OneWire@2.3.6"),
+            PackageSpec("My Private Lib@1.0.0"),
         ]
-        installed_libdeps_pkgs = LibraryPackageManager(
+        installed_env_pkgs = LibraryPackageManager(
             os.path.join(config.get("platformio", "libdeps_dir"), "private")
         ).get_installed()
-        assert pkgs_to_specs(installed_libdeps_pkgs) == [
+        assert pkgs_to_specs(installed_env_pkgs) == [
             PackageSpec("ArduinoJson@6.19.3"),
             PackageSpec("DallasTemperature@3.9.1"),
-            PackageSpec("OneWire@2.3.6"),
         ]