My laptop had Windows 8 installed. I eventually managed to get Fedora installed alongside Windows. Windows disappeared for a while but a second install of Fedora brought Windows back. It was really wierd.

So, everything on my machine is UEFI at the moment.

Now I cleared some space and want to install the Qubes OS (linix based) alongside these two. Qubes is non-UEFI.

Is this a mad idea or something that could work?

I would hope to stop Qubes installing any kind of booter, which would definitely screw up the system. I'd look to add Qubes manually to the Fedora booter (GPI).