The Qubes team advises against dual-booting, because so much trust is based on dom0’s security, which could potentially be attacked by someone who compromised PureOS while it was running. I would only recommend dual booting for someone who is already very advanced with Linux and in particular with managing grub. There are guides online you can adapt (in particular one by Micah Lee) on how to share a /boot partition between PureOS and Qubes.
Doing all of that along with PureBoot, would then ratchet up the complexity yet another level, as each time you update the OS in either Qubes or PureBoot you would need to manage resigning files in PureBoot at next boot (plus the added complexity of installing such a dual-boot system in PureBoot, the easiest path would be to set everything up, ignore PureBoot warnings about signatures, and when everything is finally set up, perform an OEM Factory Reset).
My advice if you want to try out Qubes is to go all in and install it by itself. Then after you try it for awhile if you decide it’s not for you, reinstall PureOS on top of it.