No, the limit on champions is not linked to any campaign. Dominion Campaign rules appear in Necromunda Rulebook (2018). Limit to two champions in a starting list appears under House Gang lists under Gang Composition (p11 GoTU). But this section is being replaced in each ‘House of...’ book (eg p29 in Blades, p33 in Artifice).
The replacement section in each ‘House of...’ books no longer has a limit on starting champions, beyond having an equal number of (Leader+Champion+Special Champion) to (Prospect+Ganger+Juve).
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That's a valid interpretation too.
At which point, @Vegeta365 it's down to the agreement of your group, as with so many aspects of the game.
My own reasoning was that Dominion references GotU, pg11 of which then says that all gangs follow those rules that include the limit on champions.
Yes, N18 clearly wasn't written in any expectation of the house books existing and yes, much of pg11 is reprinted in each house book while omitting the champion limit. It probably is intended for the champion limit to die off when N18 is fully obsolete/replaced but that's 4+ months away and while any gangs are still using GotU then in my opinion it needs to be a conscious decision (by group or arbitrator) whether to waive the limit for all or apply it to every 'clan-house' gang