You should be defining your resources on the Resource Sheet view, not creating them by typing their names into the Resource Names column in the Gantt chart.

If you go to the Resource Sheet view, you can enter a maximum (max unit) above 100% to indicate that you have multiple of those subcontractor resources. So if you have 4 carpenters, set the max units to 400%.

It also sounds as though you have automatic leveling on - I would set the leveling option to manual. Not all overallocations need to be fixed.