A Commom Suit Combination
The normal way to play AJxx opposite Kxxx for four tricks is to finesse. It's not always the best way to play a hand!
Try For Doubleton Queen
After losing the first four tricks, declarer cashes the A and K in one of the minor suits in case there's a doubleton Q. If that doesn't work, decalrer falls back on the finesse in the other minor.
Establish A Long Suit
Draw trumps, play three rounds of clubs ruffing in hand. If clubs break 3-3 there is no need to rely on the spade finesse.
Double Finesse
Take a finesse in clubs. In the likely event that you lose that trick, cash the ♦A and ♦K in case the ♦Q drops. You can always fall back on the second club finesse for the extra trick.
Small Chances Add Up
There's a small chance that one player holds ♣QJx. Play three rounds of clubs first to take a look before reverting to the diamond finesse.