I've posted on the Fedora forum, but no answers. Years ago there used to be a fellow there that was very helpful; guess he's moved on. Anyways here is a copy of that post:
In previous posts here I have gone on about installing Fedora 31 four times and crashing four times being booted through Mint Mate's grub. I now have had Fedora Mate 31 running smoothly for several days, but I would still like to have Mint Mate on board. Previously booting through Mint's grub; Fedora would boot well into the boot process but wouldn't finish. It would cycle back and forth between the final boot code and the log in window.
I guess my question is has any one else had a similar problem and/or are there some special considerations in this combination?

I have a Dell Inspiron 2 in one 15-5578 laptop.

I installed Fedora first with just under a 600Mib EFI partition. Then after testing and all was OK installed Mint mate. Then after a couple of days Fedora wouldn't finish the boot to login.

Personally, I don't understand what you mean by this. What do you mean by "cycle back and forth"? What is "final boot code"?

Where does it stop? Can you see an error message?

You will probably need to post more details to get help and the best way to do that if you can still boot Mint is to go to the site below and download and run the boot repair script using the 2nd option described on that page to add a ppa for boot repair. After installing, run it with the Create BootInfo Summary option. This will give you a link when it finishes which you can post here to get help as it will have many details on your system.

https://help.ubuntu.com/community/Boot-Repair

When I say "boot code" Fedora when booting up would scroll lines of code whilst booting. Now it does a quiet boot and doesn't show these lines of code.

I could see no error. It booted as normal; although now I have just Fedora installed and it doesn't scroll through code on booting. But then it did and it would reach the login page which I had set to a two second delay and then it would revert back to the final lines of boot code and then to login page again. That's what I mean by cycling (can't think of the word to use); I gues it's caught in a loop; just keeps on going back and forth between boot code and login page.

I just would like to have Mint back on, but don't want to go through Fedora misbehaving again

Does the fedora use uuids in the fstab? If so, my guess would be the uuid of the swap partition changed when mint was installed, causing the hangups.

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Wow that sounds like a possibility as they both had the same swap partition to use. So what do you think I should do as I would like to install Mint. The problem did not happen the moment I installed Mint so I have time to make some adjstments. I think with 16GB memory I don't really even need a swap partition, but I don't think Fedora will install without one.
At present I have a copy of the fstab and a backup of the EFI partition. I'm getting a little paranoid with Fedora. Last night I logged out and tried to log back in; wouldn't accept my username password combo. I had to do a live Fedora boot and run Timeshift to restore.
Thanks for your reply.

after installing mint, mint fstab should have the uuid of swap, set fedora fstab to same uuid for swap

Will do thank you; much appreciated. Will try it over the week-end.

Swap has the same uuid on both Mint and Fedora. So far no problems with both OS's installed. If it crashes on me again I'll just use Mint. One thing I'm curious about is in Fedora's boot process. I have installed it many times now and on some installs Fedora has a quiet boot to auto login; just select Fedora in Grub and the next screen I see is my desktop. Other times (as it is now) it shows the whole boot process i.e. lines of code up to loading desktop.

That is dependent on This line in your /etc/default/grub.
is what hides the boot process.
I personally like to see the boot process, so usually delete the two words.
Have to update your grub.cfg for it to take effect.

Thanks I just couldn't figure out why after installing many times; sometimes quiet load other times not.

Here's mine and it does say quiet

GRUB_TIMEOUT=5
GRUB_DISTRIBUTOR="$(sed 's, release .*$,,g' /etc/system-release)"
GRUB_DEFAULT=saved
GRUB_DISABLE_SUBMENU=true
GRUB_TERMINAL_OUTPUT="console"
GRUB_CMDLINE_LINUX="resume=UUID=ebe3c4a9-aa30-4f3b-97c9-30e9637d876e rhgb quiet"
GRUB_DISABLE_RECOVERY="true"
GRUB_ENABLE_BLSCFG=true

You need splash to get the picture, but not sure how that all works

"Machine hp-5GB memory." fedora live-X86-64 work station 31.1.9 CD runs well booted off live CD. Several distros' installed on hard-drive. Want to replace one distro with fedora. Beginning to believe it's not worth the aggravation!

I don't understand what's going on with this EFI thing, it seems to cause problems.
Replaced optical drive and wanted light iso for testing. Tried several puppy iso some with EFI it seemed Brasero, K3b had trouble with EFI iso.

Went over to fedora forum, however did not register. I'm of the opinion the best place for help is here.

So is Mint loading the Grub? Fedora has been running fine for me now. I think I may have caused the problem by putting a Noatime in fstab. Things seem a lot more complicated since UEFI came on the scene. I made a 600Mb EFI partition for Fedora which only uses 45, but I thought Mint may want more. I loaded Fedora then Mint and all seems OK; made a Home partition for Mint and a partition for Timeshift. Don't know what I'd do with all the OS's you have running though. Good luck.