Eldrazi Mimic’s ability will overwrite any other effect setting its base power and toughness. Such effects that begin to apply after that ability resolves will similarly overwrite the ability. Effects that modify Eldrazi Mimic’s power and/or toughness but don’t set its base power and/or toughness to specific values will apply no matter when they started to apply. The same is true for any +1/+1 counters it may have.