ESA Renewal + with PIP

Hello

My mother already receives ESA and was sent an assessment form to renew which I am completing.

As her condition has become worse, I was thinking of applying for PIP in parallel.

Is applying for both benefits like this advisable? or waiting until 1 or the other is completed.

TIA
Gentle

I will be keeping a copy of the ESA form so I can copy over duplicate assessment components. (few weeks left to submit)

*I understood if she wanted to claim both ESA and PIP, two assessment forms will be required regardless of when the claim is made or have I misunderstood this?

* Is there any advantage / disadvantage of having ESA / PIP assessments submitted in parallel ?

I was thinking of waiting for ESA to be awarded first, but would rather not wait due to the time it takes to process.

TIA
Gentle

and just for clarity

Receiving 0 points for ESA/PIP has no bearing on one another?