Is it possible to recruit more templar/skimishers/reapers?

I was finally able to get another Reaper through a covert action. As far as I've seen, that's the only way to get new faction-units.

You can get one extra faction soldier from the first resistance faction that you contact by using a covert action that requires high influence in that faction.

With the WotC tutorial on you always encounter the Reaper faction first making it only possible to get an extra Reaper.

I read this in another thread that said that a dev had said it during a livestream and it seemed correct my first full run of the game so I believe it to be true but if you find proof otherwise, please tell me.

I'm almost finished with my first WotC run — which I really dragged out until November with a completely empty Avatar Project progress bar. I've got exactly four faction soldiers, the three initial ones from making contact and one additional Reaper from a covert op, I think it was simply called "Recruit Soldier". Since it was my first WotC run I did actually look out specifically at every turn for faction soldiers but alas, I got only the one extra.

I had two seemingly random faction missions, but those only allowed me to get more regular soldiers, so maybe that were just a new kind of regular new resistance mission types even though they were not introduced the same as the usual ones.

There might be an resistance order giving you Skirmishers. Unfortunately, I won't be able to figure out if these guys permanently join XCOM or just work in the mission for you as it is already deep in November and XCOM is really armed to the teeth already.