Can I obtain a new F-1 CPT while H-4 is filed?

I’m currently enrolled in a Ph.D. program. I received an offer from a non-profit organization to work on the same lines as my Ph.D. I was wondering if I can apply for CPT work authorization through my school?
We applied priority H-1 for my husband, H4 and H4 EAD (Spouse I140 is approved) on 20 November 2019. His H-1 got approved. My cases (I-539 and I-765) is still pending. We requested the effective date of my CoS from Dec 19, 2019. So, Can I obtain a new F-1 CPT till I receive H4 EAD? What are my options?