You can pull too much current from a rail, but if you have a single rail design then you dont have to worry about tripping individual rails, you do still have to worry about over drawing the PSU as a whole which can damage it. What PSU do you have and what are the other specs in your system?
You say you are looking to upgrade, what are you looking to upgrade to? General rules of thumb, a good 550W unit(~40A on +12V) will power any single GPU, a good 750W unit(~60A on +12V) will power a two GPU setup, these both leave additional power to spare to keep the PSU cool and efficient.