A lot depends on which tetra. I know the little neons like their water quite soft and neutral to low pH. When I compare that to the needs of mollies or platies, I don't even try to put them together. Check the water requirements of the particular tetra that you are interested in keeping, I expect you will find many do best with the same kind of water as the neons.
Ofcourse if you want to have any chance of breeding your fish you will stay away of any larger tetra like serpae tetras. they will slaughter the fry. or anything smaller