3 flies is common with european fly fisherman who fish lakes. You don't see it much over here - even though legal on most waters.
If you do try it, chronimid fishing under and indicator would be one way. Not a lot of casting needed. Or various trolling techniques. It can be deadly if you vary your speed and allow your flies to sink to the bottom, then speed up and let them SLOWLY rise to the surface, then slow down\stop and let them sink back down - rinse, lather, repeat...
I fish 2 flies often. Dry fly with a nyph dropper. Big dry with a tiny midge. Leech\Bugger with smaller fly \ nymph trailer. Various indicator techniques with 2 egg patterns.
Using 2 flies can help add weight - instead of adding shot or using sinking lines or tips.
A dry on top can act as a strike indicator - and also attract\hook fish. And many other good reasons.
Reasons not to do it:
Some don't find it 'sporting' or 'fly fishing'
Harder to cast - need to open up the loops
You risk losing more than one fly
You risk foul hooking fish if they strike and miss the lead fly and you set the hook and snag them with the trailer...
Generally I just tie the dropper fly to the bend of the top fly's hook using a lighter weight line (and\or flourocarbon).