I am on DONE04 ex-AMM that started AMM-JFK-MIA...AKL-HKG....etc

I will have 4 segments left when I depart Asia & would like to maximize before terminating in AMM.

I'm contemplating something like: SIN-LHR-DME-MAD-LHR-AMM
which would likely require an overnite in MAD.

Any other suggestions to maximize miles -- or interesting places to stop for a day or 2?