I prefer a build of Sunfire, Abyssal, Haunting guise/Liandry's, Sorc boots + whatever you still need. Randuins is great due to increased E damage and it adds a really strong aoe slow after his ult initiation. You only need a chalice vs heavy AP lanes/heavy poke lanes where the enemy wont allow you to regen the passive back up so you have to spam that Q to trade back. Sell it later on. You are still very tanky but you can kill a squishy in a single combo if they don't build defensive items.
The full tank build only works vs AS dependant Carries and with a good team which will abuse that you zone the enemy Ad carry (aka NOT your average game).
If you really want more damage I'd rather get a gauntler than a Trinity though. Gauntlet adds more damage (AoE > singletarget) and allows you to chain more cc after your ultimate. But i've got to admit that I've only built this like once in all my malph games and that was because it didn't matter anymore.