I wouldn't try to renovate an occupied unit if that's what your asking... I would start with the vacant unit.. If no unit's are vacant check the leases (and your states landlord tenats laws) and give notice of non-renewal due to scheduled renovations, to who ever is in m2m contract. I would offer renovated unit to an existing tenant if they qualified as another way to open up a unit.
The tenats have right of peaceful enjoyment.. I wouldn't be running a wet saw at 3 am... Just use some common sense and you should be fine. I have done numerous renovations with tenants in adjacent units. To be honest they are usually happy to see improvements taking place.
I have rehabed each unit independently during natural tenant turnover, and not forced the issue. My philosophy is that if the tenants are generating income, why would I upset that? Plus, they signed the lease for the apartment "as is," so I am not obligated to upgrade the unit while they live in it. What you lose is the economy of scale when doing everything at once, but you don't artificially create 100% vacancy. As as exception, big ticket items that won't displace the tenant or their belongings are free game. I've done HVAC system replacement with occupied units because I got a huge discount by doing all of them at once. Plus, it didn't take much effort or inconvenience the tenants too much.
I've had tenants request new carpet or paint for their units, and basically told them if they are willing to move all of their furniture out of the building to do the work, then I'd consider it. That usually stops the conversation fairly quickly. Same with things like kitchen cabinets, countertops, etc. Most tenants don't want to go through the inconvenience of dealing with contractors roaming their apartments.
As for tenants rights, generally speaking, when you purchase the property, you purchase the existing leases along with it. Check the terms of the existing leases and see what you need to provide them. I agree with @Peter Bowen in that I've never had a complaint when rehabing an adjacent unit. I've offered the rehabed unit to existing tenants, but none have ever jumped on it because they don't want to go through the hassle of moving furniture or updating addresses for everything. Plus, the rehabed unit will be priced at a higher level than the others.
I had an awful inherited tenant complain about the funky cracked walls covered in paneling at the same time as she was saying her kid has asthma. Like i would start gutting walls in an occupied unit with an asthmatic! That said, reno 1 unit at a time, and don't raise the rents on the others while you have one vacant!!