Let's firstly decide whether we are OK with multiple causes of death. And for this we need to collect use cases of how people want to analyze death.
We have now that the death domain contains the clinical event for how and when a Person dies.
I.e if person committed suicide we store 'Suicide' as the cause. It's OK from some social and/or clinical
perspective. But any pathology report contains 'suicide' as cause of death: it can be asphyxia, cerebral edema, intoxication etc.
So what I think is that we definitely need to allow multiple causes of death because we may be interested in different levels of granularity. And when we are speaking about how to store - I agree with @pavgra but would like to see also something similar to condition_status_concept_id from CONDITION_OCCURRENCE table