Out of the box? Yep! I realise that will annoy people but honestly it's a good thing - any solution that would not bypass a pi-hole would allow governments and ISPs to do the same.

To retain your pi-hole, you'll need to run a DoH proxy on your pi-hole device, configure your browser to use that as the DoH provider, and this will allow your pi-hole to inspect and modify DNS results. Your pi-hole can then use any upstream DoH provider that you want.