I did some testing and found out you can use larger than the rated wires in most Posi-Products. When doing this, I recommend you strip the wires just enough to slightly protrude from the Posi-Lock when the wire is pushed into it as far as possible. You don’t want too much of the strands of wire in the Posi-Lock, as there isn’t enough room for them. Also, you must spread the strands evenly around the perimeter of the Posi-Lock.
PL1824 - this little Posi-Lock can work with up to 16 AWG wire. Note, this Posi-Lock should not be tightened too much or the threads will strip. Snug the cap up by hand only.
PL1416 - this Posi-Lock is amazing and can actually work on 12 AWG wire. This Posi-Lock is very tough and you can tighten the cap up by hand as tight as possible. Ok, some gorillas out there might strip the threads, but I found I could tighten this little guy up really really tight.
I’m sure others such as the PL1012 can also work with larger wires. If the wire insulation will physically fit into the cap opening, you can likely use that wire in the Posi-Lock. The PL1012 can be tightened with pliers to really lock a wire into it. It’s tough and of course has larger threads.
Here’s some photos of a PL1416 joining two large 12 AWG wires. I tested this connection by pulling apart as hard as I could and it held. As a bonus, the wire practically seals in the cap because its insulation size fills the opening. If your wire has extremely stiff strands this may not work.