I work as a paramedic in a 40 bed Level II trauma center with about 60k visits a year. We frequently have multiple high acuity patients (level 2 or 1 on the ESI triage scale).
Our current staffing is 4 patients : 1 nurse. We have PCA who transport, stock, change bedpans, and a lot of other tasks. They are involved with patient care but mostly do the nurses scut work. There are two or three PCA on the floor.
Our department runs smoothly though because of how paramedics are utilized. We triage, start lines, administer IV meds, intubate (not unusual when we are single coverage doc and the crap hits the fan), splint with orthoglass, and we do take patient assignments when nursing staff is down or the need exists. I really do think of us as the swiss army knife of the ED. There are a few things we cannot do for legal reasons but not a big deal. Typically there are two medics on the main floor and two on the quick care side.
As far as optimal staffing goes, it appears that 3:1 is what many ED in my area are going for with proper ancillary staffing. I am not sure of any studies out but our satisfaction scores have skyrocketed with going from a 6:1 to 4:1 staffing and adding additional staff on. Purely anecdotal but there may be something there.