What will happen to GRUB when you install Ubuntu alongside another Ubuntu installation?
If you install a version of Ubuntu with an older version of Grub, then install another Ubuntu alongside it with a newer version of Grub, what’ll happen? Will the newer version overwrite the other, or will they just be side by side?
The reason why I’d wanna know because I want to dual boot Elementary OS and Linux Mint along with Windows 7
If you install a second Ubuntu, the bootloader of the first installed Ubuntu will be usually overwritten, the grub version does not matter at all. But it depends on how you install. With default settings, the bootloader will be overwritten.
Also your hardware configuration (which we don’t know about) matters, single disk or multiple disk is not the same and usually you can configure the bootloader location during installation.
What you want to do is different (dual boot Mint with Elementary), it may depend on boot mode (UEFI vs legacy) and will depend on the grub configuration of the distribution. Also there should be a way to configure this the way you want during or even after installation.
Details about Mint and Elementary are off-topic and not supported here.