Do multiple influences on a map stack?

I am trying to juice up this map as much as possible for the lulz. if I add an elder scarab and run it in the warlord influence area, will the map have 3 influences with extra mobs from each influence?

Pretty sure you cannot have multiple influences on a map. It's not even a matter of Awakening Orb since map influece is an implicit rather than an actual influence.
Opening a Shaper- or Elder-Influenced map on an occupied region should bypass the Conqueror occupation and run the map only Shaper- or Elder-Influenced.
Furthermore, it's not possible to have a map both Shaper- and Elder-influenced Via Scarab+Implicit influence,

A certain user reported a bug, however, in which using a Shaper/Elder scarab on an occupied region would make the Conqueror progression go on. Perhaps this has some unexpected results when hitting the middle or last phase with actual extra packs and influence from the Conqueror?

I've played this map in a warlord influenced area. It had both the warlord mobs spawning and shaper randomly appearing and doing his attack. Can somebody test this?

Yes, you can have two influences active at the same time, one from the atlas itself and one from scarabs.

This was changed in Delirium 3.10.1:
https://www.pathofexile.com/forum/view-thread/2809244

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Areas that have Conqueror Influence can now also have either Shaper or Elder Influence applied to them.

Welp, missed that bit during Delirium. Thank you, Scarletsword, I'll keep it in mind...
Time to shoot out a lot of Shaper scarabs that were just taking space.