I agree with @DavidH, the best technical description is multiple (consecutive) zwischenzugs. As for a more specific term, I don't know an established one either, so maybe it's time to invent one. I propose to call the scenario you describe a caterpillar (line), after the famous picture book by Eric Carle, The Very Hungry Caterpillar. According to Wikipedia:
The book features a very hungry caterpillar who eats his way through a wide variety of foodstuffs before pupating and emerging as a butterfly.
I've used this image in teaching, and it tends to work very well, especially if it's a pawn who does most of the capturing. Here's one of my favorite examples:
[Event "Stuttgart simul"]
[White "Tal, Mihail"]
[FEN "2r1k2r/1p1bppb1/p2p1np1/q3n1p1/3NP2P/2N1BP2/PPPQB3/1K1R3R w k - 0 15"]
[Source "Schach 10/1994, p. 69"]
1. hxg5 Rxh1 2. gxf6! Rxd1+
3. Nxd1! Qxd2 4. fxg7! 1-0
That former h-pawn turned out to be a very hungry caterpillar indeed. Black resigned just when the beautiful butterfly was about to emerge on g8.