Yes, they are limited. 1 at Clan Tier 2 (lowest seen AI Clan Rank), 2 at Rank 3, 3 at Rank 4+. It is opaque as to if the Clan Leader perk for +1 party would even work, but it is extremely unlikely they would get the skill rank to earn it.
You will most commonly see the above demonstrated when you form a Companion -> New Clan, as such new clans start at Rank 2.
Hope that helps.
**EDIT** Emperor1997 got it right, and I had it mistaken. Read down for their find, please.