Do you ever go to the gym? We could go together.
'Palestra' = pa-LE-stra, stress on second syllable. 'Potremmo' = po-TREM-mo.
Use this to combine a social plan with a fitness activity. Gym buddies are an important feature of Italian social life. Asking if they go to the gym first, then proposing going together, is tactful and considerate.
'Potremmo' (we could) is the first-person plural conditional of 'potere' — softer and more hypothetical than 'possiamo' (we can). 'Andarci' = 'andare + ci' (go there) — 'ci' replaces the location already mentioned.
Ti alleni la mattina o la sera?
Do you train in the morning or the evening?
Finding a compatible schedule
Potremmo iscriverci nella stessa palestra.
We could sign up at the same gym.
Long-term plan rather than a single visit
Facciamo una corsa insieme domani mattina?
Shall we go for a run together tomorrow morning?
Running together as alternative to gym
Italian gym culture ('cultura della palestra') is intensely social. Regular gym-goers often develop close friendships with regular training partners ('compagni di allenamento'). Italians tend to chat between sets, share nutrition advice, and celebrate each other's fitness achievements. The gym is as much a social space as a fitness facility.