Is there a way for my sim to own 2 apartments in an existing apartment building?

No, your Sim cannot own more than one residence. If you have Get to Work, Cats & Digs, Dine Out, or Business & Hobbies, you can own a second lot as a business, but it has to be that pack’s business lot type. If you own For Rent there’s a special “residential rental” lot type that can make multiple apartments on one lot and lets you own that, but only if it’s a lot with that lot type and only if you own the whole lot.