diff --git a/upath/core.py b/upath/core.py
index 7c28ba00..d572a4c9 100644
--- a/upath/core.py
+++ b/upath/core.py
@@ -1221,10 +1221,17 @@ def copy(self, target: _WT | SupportsPathLike | str, **kwargs: Any) -> _WT | UPa
         """
         Recursively copy this file or directory tree to the given destination.
         """
-        if not isinstance(target, UPath):
-            return super().copy(self.with_segments(target), **kwargs)
-        else:
-            return super().copy(target, **kwargs)
+        if isinstance(target, str):
+            proto = get_upath_protocol(target)
+            if proto != self.protocol:
+                target = UPath(target)
+            else:
+                target = self.with_segments(target)
+        elif not isinstance(target, UPath):
+            target = UPath(target)
+        if target.is_dir():
+            raise IsADirectoryError(str(target))
+        return super().copy(target, **kwargs)
 
     @overload
     def copy_into(self, target_dir: _WT, **kwargs: Any) -> _WT: ...
@@ -1238,10 +1245,19 @@ def copy_into(
         """
         Copy this file or directory tree into the given existing directory.
         """
-        if not isinstance(target_dir, UPath):
-            return super().copy_into(self.with_segments(target_dir), **kwargs)
-        else:
-            return super().copy_into(target_dir, **kwargs)
+        if isinstance(target_dir, str):
+            proto = get_upath_protocol(target_dir)
+            if proto != self.protocol:
+                target_dir = UPath(target_dir)
+            else:
+                target_dir = self.with_segments(target_dir)
+        elif not isinstance(target_dir, UPath):
+            target_dir = UPath(target_dir)
+        if not target_dir.exists():
+            raise FileNotFoundError(str(target_dir))
+        if not target_dir.is_dir():
+            raise NotADirectoryError(str(target_dir))
+        return super().copy_into(target_dir, **kwargs)
 
     @overload
     def move(self, target: _WT, **kwargs: Any) -> _WT: ...
@@ -1274,8 +1290,15 @@ def move_into(
             raise ValueError(f"{self!r} has an empty name")
         elif hasattr(target_dir, "with_segments"):
             target = target_dir.with_segments(target_dir, name)  # type: ignore
+        elif isinstance(target_dir, PurePath):
+            target = UPath(target_dir, name)
         else:
             target = self.with_segments(target_dir, name)
+        td = target.parent
+        if not td.exists():
+            raise FileNotFoundError(str(td))
+        elif not td.is_dir():
+            raise NotADirectoryError(str(td))
         return self.move(target)
 
     def _copy_from(
diff --git a/upath/implementations/local.py b/upath/implementations/local.py
index 739c78aa..3bf3ec76 100644
--- a/upath/implementations/local.py
+++ b/upath/implementations/local.py
@@ -21,6 +21,7 @@
 from upath._chain import ChainSegment
 from upath._chain import FSSpecChainParser
 from upath._protocol import compatible_protocol
+from upath._protocol import get_upath_protocol
 from upath.core import UnsupportedOperation
 from upath.core import UPath
 from upath.core import _UPathMixin
@@ -377,10 +378,17 @@ def copy(
             # hacky workaround for missing pathlib.Path.copy in python < 3.14
             # todo: revisit
             _copy: Any = ReadablePath.copy.__get__(self)
-            if not isinstance(target, UPath):
-                return _copy(self.with_segments(str(target)), **kwargs)
-            else:
-                return _copy(target, **kwargs)
+            if isinstance(target, str):
+                proto = get_upath_protocol(target)
+                if proto != self.protocol:
+                    target = UPath(target)
+                else:
+                    target = self.with_segments(target)
+            elif not isinstance(target, UPath):
+                target = UPath(target)
+            if target.is_dir():
+                raise IsADirectoryError(str(target))
+            return _copy(target, **kwargs)
 
         @overload
         def copy_into(self, target_dir: _WT, **kwargs: Any) -> _WT: ...
@@ -398,10 +406,15 @@ def copy_into(
             # hacky workaround for missing pathlib.Path.copy_into in python < 3.14
             # todo: revisit
             _copy_into: Any = ReadablePath.copy_into.__get__(self)
-            if not isinstance(target_dir, UPath):
-                return _copy_into(self.with_segments(str(target_dir)), **kwargs)
-            else:
-                return _copy_into(target_dir, **kwargs)
+            if isinstance(target_dir, str):
+                proto = get_upath_protocol(target_dir)
+                if proto != self.protocol:
+                    target_dir = UPath(target_dir)
+                else:
+                    target_dir = self.with_segments(target_dir)
+            elif not isinstance(target_dir, UPath):
+                target_dir = UPath(target_dir)
+            return _copy_into(target_dir, **kwargs)
 
         @overload
         def move(self, target: _WT, **kwargs: Any) -> _WT: ...
@@ -432,8 +445,15 @@ def move_into(
                 raise ValueError(f"{self!r} has an empty name")
             elif hasattr(target_dir, "with_segments"):
                 target = target_dir.with_segments(str(target_dir), name)  # type: ignore
+            elif isinstance(target_dir, pathlib.PurePath):
+                target = UPath(target_dir, name)
             else:
                 target = self.with_segments(str(target_dir), name)
+            td = target.parent
+            if not td.exists():
+                raise FileNotFoundError(str(td))
+            elif not td.is_dir():
+                raise NotADirectoryError(str(td))
             return self.move(target)
 
         @property
diff --git a/upath/tests/cases.py b/upath/tests/cases.py
index dddb9852..22587fa9 100644
--- a/upath/tests/cases.py
+++ b/upath/tests/cases.py
@@ -551,6 +551,40 @@ def test_copy_local(self, tmp_path: Path):
         assert target.exists()
         assert target.read_text() == content
 
+    @pytest.mark.parametrize("target_type", [str, Path, UPath])
+    def test_copy_into__file_to_str_tempdir(self, tmp_path: Path, target_type):
+        tmp_path = tmp_path.joinpath("somewhere")
+        tmp_path.mkdir()
+        target_dir = target_type(tmp_path)
+        assert isinstance(target_dir, target_type)
+
+        source = self.path_file
+        source.copy_into(target_dir)
+        target = tmp_path.joinpath(source.name)
+
+        assert target.exists()
+        assert target.read_text() == source.read_text()
+
+    @pytest.mark.parametrize("target_type", [str, Path, UPath])
+    def test_copy_into__dir_to_str_tempdir(self, tmp_path: Path, target_type):
+        tmp_path = tmp_path.joinpath("somewhere")
+        tmp_path.mkdir()
+        target_dir = target_type(tmp_path)
+        assert isinstance(target_dir, target_type)
+
+        source_dir = self.path.joinpath("folder1")
+        assert source_dir.is_dir()
+        source_dir.copy_into(target_dir)
+        target = tmp_path.joinpath(source_dir.name)
+
+        assert target.exists()
+        assert target.is_dir()
+        for item in source_dir.iterdir():
+            target_item = target.joinpath(item.name)
+            assert target_item.exists()
+            if item.is_file():
+                assert target_item.read_text() == item.read_text()
+
     def test_copy_into_local(self, tmp_path: Path):
         target_dir = UPath(tmp_path) / "target-dir"
         target_dir.mkdir()
@@ -581,6 +615,32 @@ def test_copy_into_memory(self, clear_fsspec_memory_cache):
         assert target.exists()
         assert target.read_text() == content
 
+    def test_copy_exceptions(self, tmp_path: Path):
+        source = self.path_file
+        # target is a directory
+        target = UPath(tmp_path) / "target-folder"
+        target.mkdir()
+        # FIXME: pytest.raises(IsADirectoryError) not working on Windows
+        with pytest.raises(OSError):
+            source.copy(target)
+        # target parent does not exist
+        target = UPath(tmp_path) / "nonexistent-dir" / "target-file1.txt"
+        with pytest.raises(FileNotFoundError):
+            source.copy(target)
+
+    def test_copy_into_exceptions(self, tmp_path: Path):
+        source = self.path_file
+        # target is not a directory
+        target_file = UPath(tmp_path) / "target-file.txt"
+        target_file.write_text("content")
+        # FIXME: pytest.raises(NotADirectoryError) not working on Windows
+        with pytest.raises(OSError):
+            source.copy_into(target_file)
+        # target dir does not exist
+        target_dir = UPath(tmp_path) / "nonexistent-dir"
+        with pytest.raises(FileNotFoundError):
+            source.copy_into(target_dir)
+
     def test_read_with_fsspec(self):
         p = self.path_file
 
diff --git a/upath/tests/implementations/test_data.py b/upath/tests/implementations/test_data.py
index a9e2f4b8..d478559f 100644
--- a/upath/tests/implementations/test_data.py
+++ b/upath/tests/implementations/test_data.py
@@ -253,3 +253,8 @@ def test_unlink(self):
         # DataPaths can't be deleted
         with pytest.raises(UnsupportedOperation):
             self.path_file.unlink()
+
+    @overrides_base
+    def test_copy_into__dir_to_str_tempdir(self):
+        # There are no directories in DataPath
+        assert not self.path.is_dir()