Board limit # of units a single renter may occupy?

Can't you go after them for running a commercial business out of an apartment?

Sorry, but you're SOL.

If you want control over what your neighbors do, buy into a co-op.

couldn't you amend the bylaws to prohibit commercial business in apartments (to the extent it is even allowed) or add a limitation that a single party and its affiliates may only rent a single apartment.

That's almost certainly not permitted by zoning, the building code, or the C of O. Talk to a lawyer, but the board should be able to invalidate the leases on those grounds as long as there's a majority that sides with you.

Check the bylaws and the offering plan. There may be limits on renting out residential units as professional or commercial space.

Not sure but day care with a license from NYS has different rules from most commercial businesses.

The condo's governing documents are written by the sponsor so as to preserve its maximum flexibility. E.g., the usual language saying unsold units can be used for "any lawful purpose."

The ringer is what "lawful" means, so there's always room to spend money on lawyers to dicker over that.

I'd bet the sponsor is going exactly as far as it can.