Can I connect three wires using a screw terminal?
Putting multiple wires into one side of a connector is what everybody does.

It does mean that it can be a bit tricky to get all the wires pushed in at the same time to the right depth.

With stranded wires, there are rarely any problems. Twisting them together before pushing them in can help with alignment.

With solid wires, there can be configurations of 'a few' wires that leave one of the wires not properly clamped, if the others form a stable arrangement and take the screw clamping force like an arch. Be aware of that as a failure mechanism to look out for. 

If you really want a one-wire-per-screw arrangement, then you could permanently wire a link along the 'backs' of several connectors, and use one wire each to the front.