I know. What I'm trying to say is, you're not asking them to change the contract for you. You're asking them to change the contract for both of them.

If you ask a prospective employer to remove any clauses that say "Any work done during employment is ours" then why should they bother? They put this clause in to a) avoid being the funder for work that doesn't benefit them and b) Ensure you don't steal other company resources.

If you suggested "Can we please add a clause that states any work done outside of contracted hours using resources not directly owned by the employer shall remain the property of the employee" that would seem much more reasonable.