Is it Possible to Overload SQL Server Functions?
There is no straight-forward way of carte-blanche overriding a built-in function in SQL Server.

You can kind of fake it by creating a function with the same name in a different schema, then calling that function with the schema name, as in:

SELECT dbo.COUNT(1)
FROM dbo.SomeTable st
GROUP BY st.SomeCol;


However, this is quite likely to cause more confusion than it is worth.