Top of the Heap focused on the attempts of two minor Married... with Children characters—Charlie Verducci (Joseph Bologna) and his son Vinnie (Matt LeBlanc)—to get rich.

Charlie's "master plan" is for Vinnie to marry into a wealthy family; to this end, the two Chicago slum residents try to get into high society.

In some episodes actors from Married... with Children made guest appearances as their characters from the show, thus reinforcing the connection between the two series.

[citation needed] The only characters returning in this version were the eponymous Vinnie (Matt LeBlanc), Mona Mullins (Joey Lauren Adams) and Bobby Grazzo (Robert Torti), who only appeared in the last episode of Top of the Heap.

Charlie has a hard time convincing Vinnie that he didn't sell their cat, Mr. Fluffy, to pay for the television he claims to have won.