I have Jessie i386 on a SSD and Stretch i386 on a HDD and decide to install Stretch amd64 to a new partition on the HDD. Each drive had a swap partition. The install went okay but afterwards the UUID's for the swap partitions got changed and booting was really slow as the swap partition UUIDs no longer agreed with what was in fstab.
After a LOT of reading, I found the solutions. I needed to correct fstab for each installation, change the /etc/initramfs-tools/conf.d/resume file to agree with the new UUID in fstab, and then run update-initramfs -u on each install. What a pain.
I have no idea if the changes to the UUIDs and resulting erros in fstab were a result of something I did wrong during the install of Stretch amd64 to the new HDD partition or if it is some kind of error in the installation script. But it was a huge learning experience. Has anybody else had a similar experience?