If you have to use conductors larger than a device's screw terminals will allow, get some barrier strips and double up there.


The following image doesn't show what you'd use, but it shows how you'd mechanically do it.

A certain size wire at the left goes to your device.
There are shorting bars or shorting pieces of wire from one screw to the next screw on each strip. This gives you multiple screws you can connect your other wires to, allowing doubling up.

FYI it's easier to do this with this kind of strip than with the euro strips because the euro strips are harder to daisy-chain.