Add virtual `extends` clause during IFileElementType#parseConents()?

I have subclasses of JavaParserDefinition, IFileElementType, etc. and all is working fine.  I want all the psi classes in the context of this custom Java file type to implicitly extend another class, so in my implementation of IFileElementType#parseContents() I'd like to inject a light extends clause into the classes, if possible.  For instance, I'd like to change this class:

class Foo {

}

to behave like this:

class Foo extends com.abc.Bar {

}

Is this possible?  I've been experimenting with manually inserting CompositeElements and rolling my own "light" PsiJavaCodeReferenceElementImpl etc. to no avail.