SEER has little to do with EER. (yes, all other things being equal, higher EER will increase SEER). You gain SEER by being efficient when full btu output is not necessary after room temp and humidity is reduced.
EER on most inverter variable speed compressors (most modern mini-splits) is worse than a conventional air conditioner, since EER is specified at full rated btu. If you buy an undersized mini-split for indoor area, you will get less efficiency than an undersized, similar btu capacity conventional air conditioner.
Primary reason mini-split EER rating is worse than conventional unit is due to the three-phase inverter having about a 10% power loss at full btu output. Most mini-splits also have a smaller outside condenser heat exchanger than a conventional split unit air conditioner.
On a properly sized unit for the air-conditioned area, once area is cooled and humidity brought down, the required btu load drops to 20-30% of peak btu capability. This is where variable speed compressors shine and you get the higher SEER numbers.