Hi,
it took me a while to figure out what the installer does to get solus 4 (MATE in my case) into an UEFI GPT multiboot system. I have never seen this before, but maybe that's a new and innovative way how things are done nowadays:
a) it does not populate /boot
b) it stores no kernel or initrd in /
c) instead, it goes ahead and creates directories and files in your EFI partition, hoping that your BIOS will recognize it as a new valid boot option.
Now actually point c) didn' work so well in my case. For whatever reason I got no new/additional boot entry in my UEFI BIOS. I usually automatically boot another linux (OpenSUSE to tell you the truth), where I use grub-customizer to detect / update / customize all my OS and populate my boot menu and options. I had to user Window's (yukk) EasyUEFI (or else you can do with efibootmgr) to remove some of that stuff and clean up my EFI partition.
Now I was able to get back into OpenSUSE, but to my surprise, grub-customizer didn't see solus because of (a) and (b). It does not look into the EFI partition, and you may say that's what he should do. Now I know of no other OS whose installer would dare to do what solus is doing.
Can you recommend a standard approach how one would be allowed to continue to use another (non-solus) OS boot option and get it to be recognized from there (I'm pretty sure that even grub's os-prober wouldn't see solus).
I used a pretty ugly approach to get things sorted out (at least for now, as my method won't survive the next kernel update in solus).
I installed solus in a VBox machine (with msdos mbr, not uefi) and copied /boot and the two root files over to my solus partition. Alternately, you can probably go and grab most of that stuff also from the EFI partition. Next, running grub-customizer would show up an entry for Solus 4 Mate, but it's unbootable (probably because of the wrong UUIDs, hd and partition numbers from your VBox install). Go and fetch the right UUID and other options from the configuration stored in the EFI partition and update the Solus boot entry accordingly.
After that I was able to boot Solus through OpenSUSE's grub.