an external population with which to mediate the process.
Mediate how exactly? They still can't contribute to the "gene pool" since there is no pool. Asexual reproduction involves no transferral of genes within a generation, only from parent to child.
would the group go through a smaller or greater number of mutations?
On average, for the same number of generations, they would go through the same number of mutations. (This is of course disregarding things that would directly damage DNA ("free radicals")). The only effect that having them "inbred" (you really need to see this), in a lab is that the researchers can monitor and control the whole process.
There was also no theoretical reason for monopoles _to_ exist.
I think the point the GP was making was that there was no reason that they couldn't exist...
Don't steal; thou'lt never thus compete successfully in business. Cheat. -- Ambrose Bierce