compromise on (something)
To reach an agreement in which both sides make concessions. Living in this seedy neighborhood is not something I'm willing to compromise on. We couldn't agree on what to have for dinner, so we compromised on tacos tonight and Italian tomorrow.
compromise on someone or something (with someone)and compromise (on someone or something) with someone
to reach agreement with someone on a disputed matter concerning someone or something; to make concessions to someone on some point concerning someone or something. I intend to compromise on this matter with them. Are you going to compromise with me on this issue?