Is there a phrase for the generation that is taking care of three generations of family members?

The phrase "member of the sandwich generation" refers to a person who is taking care of children and elderly parents.

Is there a phrase (or word) for a person who is taking care of parents, children and grandchildren? Or grandparents, parents and children?

Example: Alice and Tom are members of the ___________ generation; they are taking responsibility for her grandmother, his mother and their three young children.

Edit in response to comment of dwjohnston:

I have not seen an article about this phenomenon, but that doesn't mean there aren't any. I have seen this referred to several times in articles about the sandwich generation (SG) as an extension of the SG problem. As more people live into their 90s, this will become more common (although one hopes not of long duration for any one care-giver.)

Solution 1:

I've never heard of one, but I'd like to propose one - "the club sandwich generation"!

Solution 2:

We call it being served a Dagwood, because that is even bigger than a club sandwich. I'm a single father with two kids taking care of my father's estate while my mother has Alzheimers and one sister bounces in and out of psychosis.

The three generations could be parents and grandparents, but remember that there are people taking care of siblings as well as children and parents.

Solution 3:

Both Clubs and Dagwoods also qualify as “Double-decker sandwiches,” and going with that term would even set the stage for using “Triple-deckers" if life expectancies continue to increase (although the definitions below from ‘Random House Kernerman Webster's College Dictionary’ via ‘The Free Dictionary by Farlex’ seemingly make no distinction between the double and the triple-deckers).

dou′ble-deck′er n.
1. something with two decks, tiers, etc.
2. a sandwich of three slices of bread and two layers of filling.

tri′ple-deck′er n. a sandwich made of three slices of bread with two layers of filling; club sandwich.

Alice and Tom are members of the double/triple-decker generation; they are taking responsibility for her grandmother, his mother and their three young children.