Manchester City's quadruple quest will see them come up against Brighton and Hove Albion in the FA Cup semi-finals, while Wolves and Watford will contest the other last-four showdown.
City scraped through against Championship side Swansea City on Saturday, winning 3-2 thanks to a late and controversial Sergio Aguero header having fallen 2-0 down in the first half.
Pep Guardiola's men have already won the EFL Cup and are also still in the hunt in the Premier League and Champions League.
Brighton had to go all the way to penalties against Millwall in their quarter-final, as they came back from 2-0 down to draw 2-2 after 120 minutes, eventually triumphing 5-4 in the shoot-out.
Wolves will undoubtedly be relieved to have avoided the Premier League champions having dealt with the similarly tricky task of Manchester United in the last eight.
Goals from Raul Jimenez and Diogo Jota were enough to beat Ole Gunnar Solskjaer's men 2-1 at Molineux on Saturday.
Watford defeated Crystal Palace 2-1 to book their place at Wembley.
The matches are due to take place at England's national stadium on April 6 and 7.