Nah you don't want 10 dungeons a week.
First few weeks just one was completely fine and maybe you want to start considering doing 4 now, but the chances of you not getting a upgrade from the vault are pretty darn slim currently.
In a month or two when you are aiming for much more specific items/slots doing 10 might be a significant benefit, but by that time you can also just blast +15s out at least twice as fast as you can today.