If I know a Sim who has a partner, but I want my Sim to be that Sim's partner, can I make them break up? For example, if I romance it hard enough, will an option like "ask to break up with partner" or similar become available? Or is it impossible?
Yes, it is possible to make other Sims break up. If you perform enough romantic actions with the Sim you are interested in, you will have the option of asking that Sim to break up with his or her partner, assuming the Sim in question is now a "Romantic Interest", as opposed to "Friend", "Good Friend" or "Best Friend". You will then be able to ask them to go steady, propose to them and eventually marry them.
Keep in mind that by asking a Sim to break up with their partner, you automatically make yourself an enemy of that now ex-partner.