Customizing Password Reset endpoint

When a user clicks “Reset Password,” is it possible to POST to a different URL than the internal Auth0 one?

What I would like to do is
a) The user clicks the button and it POSTs to my API
b) We do some internal handling
c) a Password Reset ticket is created, and use our custom emailer
d) the user gets the email

I don’t see a way to customize that request, though, just the actual email (which we’d need to setup Sendgrid or something for).