Claiming PIP and ESA at the same time

I've just submitted my PIP application. I think I qualify for ESA as well. Should I try to claim that now or wait until I have a decision re PIP? I wondered if DWP might think it's suspicious if I try to claim for both.

Hi Anneilla

Thousands of claimants claim ESA/UC and PIP. Go ahead. The DWP won't view it suspiciously.

BIS