If you have 6X6 amp light circuits you have 36 AMPS and cannot use 14 which is limited to 15 AMPs. Are you sure you are not meaning 6 or 60 Watts? that would be much more logical. .

We need much more help from you.

What type of lights are we talking about?

How do the three wall switches relate to the circuit? Are they two three way switches and one four way switch. So that any single switch could control all of the lights.

Lamps are normally wired in parallel, not serially. So that the amperage would not be additive. Each lamp would receive the same amperage.

Each lamp draws 6 amps in parallel is still 36 Amps, 4320 watts@120VAC, no different than plugging in 6 X 6 amp lights into receptacles and they are in parallel. .