It really depends on what the code variation is, and it can often be a code smell, but I like just adding a flag to the method for simpler cases of this. No complexity or overhead, easy to reason and debug, and you can retain the current method signature with a default-case call to the new method, so no other refactoring required.

It can be inelegant, clunky, and terrible practice if you're doing two totally different things in the method, but I've had a lot of cases recently where it was a nice simple solution that made sense in the context we used it.

For me, one time I like that we use simple OO is a 'DeletedMyClass' extending 'MyClass'- it does everything the same, just has a DeletedDateTime property. A few pages will do an 'is' check (we use C#) and render certain things differently, but apart from that, they both get passed around interchangeably. You could argue you could add an IsDeleted flag, but the default case is that most things we deal with are not deleted, and they shouldn't have to even know about that concept. So to me this is a very useful minimal case of OO.