As you know, ROP of lactic acid has used tin (II)2- ethylhexanoate or stannous octoate (Sn(Oct)2) widely as a catalyst. This catalyst was good with regard to high reaction rates, solubility in the monomer and the ability to give high average molecular weights.
Initiators in ROP play an important role. In this interesting paper, the researchers used 3 different alcohols & obtained variations in both the number average molecular weights & the weight average molecular weights of PLA:
I know that an initiator differs from a catalyst & your question is about varying the amount of catalyst . The given research paper opens the door for hope & I guess that lowering the concentration of the catalyst may not decrease the average molecular weight but may increase it. Only an experiment will prove or disprove my guess.