He can do whatever you want him to do, really. Death should come knocking again soon.
In the case of the Grammars, he came for Victoria Andrews, then Beau Andrews and then Gobias. He collected one of them, then had a day off, then returned for the next one, then had another day off, then came for the last of them. So in the space of a week, my household almost halved, and I had to press gang one of the Gen 2ers to do the portrait, sculpture and photo for the founder's eldership, as I didn't want to run the risk of Grimm coming very early for her.
I wondered for a few moments if I should leave out tea and crumpets for his visit two days after that, then realised that would be my founder he'd be coming for, so I ate all the crumpets that would have otherwise been left for Grimm.
The crumpets were tasty, in case anyone was wondering.
So yes, Grimm sometimes keeps coming back for more. At least now, Grimm won't be bothering my family until my four teens become elders.