Change of employer during CAP-GAP......!!!!

Dear Members,

I am currently on OPT and working for Employer X for the past 10 months

Employer Y filed H1B visa and it was picked in the lottery (H1B Cap 2018) and has an start date of OCT 1 2017.

My current work status is OPT/CAP-GAP and have applied for OPT extension with Employer X already

My question is

  1. Is it possible to change to another new Employer Z till Sep 30 and whether I get new I-20 with the employer Z

Waiting for your reply and thanks in advance.