Halo is absolutely perfect for a BR-style upgrade to the multiplayer, and an open-world upgrade in general.
The Silent Cartographer -- the most distilled Halo experience -- is already practically a mini-open world.
Now imagine the whole Halo ring as your map, and you choosing to ODST hot-drop in wherever you want to rescue stranded Marines while Covenant forces also invade. As you successfully evacuate Marines back to your heavily crippled UNSC capital ship in close orbit, you slowly upgrade and expand your capabilities, unlocking weapon pod deployments, Marine support, Warthog drops, Pelican extractions, etc.
As your capabilities expand, so do those of the Covenant forces invading the ring.
Add-in some kind of Shadow of Mordor-esque nemesis system for high ranking Covenant.
Add-in some kind of "live" mode where other players log in as either Covenant, or UNSC grunts, or other Spartan teams for PvPvE action, with Destiny-style public events.
Forget the stale linear story-levels and ancient TDM variants. Halo needs to evolve, and it can do so while staying true to what made it uniquely great in the first place; large-scale open ended combat against dynamic enemies in an incredible sandbox.