It's possible. It would require a lot of patience & perhaps also some ingenuity.
Ideally you would want a large room, so you could mic it as though it had a full string section, & for each new take, move the players to new seats.
Note whilst doing this you would run out of seats for the basses long before the violins. Bear that in mind as you arrange your tracking.
Consider also, whether for a full arrangement, it would continue to just be 4-part, or whether a fuller arrangement could be contemplated... also whether you ought to consider a bass, not just cello at the bottom end. You could score this in advance, or depending on the players, let them wing it & see what happens.
Not having the above wouldn't preclude you trying, but would limit the 'expanse' of the final recording.
Try moving the mics slightly between takes; get the players to handle the performance differently - perhaps suggest they could mimic different styles per take - things to make each take sound different. Part of the overall sound of a large section is the differences in each performance, contributing towards the whole.
The one thing you will not really be able to fake, except perhaps to some extent with EQ, is that not only each player in a large section will sound different, but their instruments will also have different timbres.
You might think about adding very subtle amounts of short echo to increase the apparent number of players [I would keep it wider than the real instruments' panning to give it further distance], but personally I would spend the time getting as many takes as you can.
You can gain apparent width in multi-tracks by panning in an arc [not a flat line] across the sound-field, bearing in mind where each instrument's 'home' would be in a large orchestra - though putting 2nd violins on the right can be interesting.
Avoid spreading the basses too far, keep them just right of centre.
Also, I would avoid the temptation to use chorus... it has a distinctive sound. OK for pop, maybe, but I would avoid it for anything vaguely approaching classical.