It's do-able, but will depend a lot upon where you are whether this makes sense or not.
Taking the EASA regime, for example, there are basically three ways you could do this:-
(1) Buy a cheap sub-ICAO aeroplane, say a Jodel, for hour building but do the PPL and CPL courses in more sophisticated CofA Aeroplanes suitable for purpose.
(2) Buy a slightly more expensive but still simple CofA aeroplane, say a C152, for the PPL and hour building, but then use a school aeroplane for complex part of the CPL course.
(3) Buy a complex SEP single, say a Piper Arrow, and do everything except the ME/IR bit in that.
I think that (1) or (2) make potentially good sense as you probably will save money, and also will learn a lot about aviation from jointly owning an aeroplane that wouldn't otherwise. (3) Will probably bankrupt you. I'd not even contemplate buying a multi-engine.
If all four of you are substantially new to aviation however, you do really want somebody more experienced as an expert partner - that may be the flying school itself, or it may be an experienced private pilot happy to own 1/5th of the asset for their own flying, for example. But I wouldn't recommend a group of people with minimal flying experience buying an aeroplane between them to learn on without expert support - there are just too many expensive mistakes to be made.