Every enhancement shaman can consume every other enhancement shaman’s primal primer debuff. Additionally, only 1 primal primer debuff can be active on a target at any given time. If multiple enhancement shamans are present with the azerite trait, then all will contribute to the first debuff applied (but only the person who applied that debuff can benefit from it - other enhancement shamans will consume it (whether they have the trait or not) without gaining any bonus damage).
When a primal primer debuff has multiple contributors, its bonus damage calculation also seems to break down (from testing on the PTR with 3.56% versatility and 34.8% mastery, if I applied 4 primal primer stacks @ +210 per application, and another person applied 4 primal primer stacks on top of that @ +174 per application (+1536 total in the pool, in theory), then my base lava lash (4002 damage) should rise to ~6146 (4002+1.348x1.0356x1536), but it only went up to ~5946 or so (implying that I was only getting +138 bonus or so per stack from the other enhancement shaman’s contribution).
This bug is difficult to reproduce in-game since it is unlikely for 2 or more enhancement shamans to be present.