I have a 500gb ssd on which I plan on running three distros, Ubuntu, Fedora and Kali. What I want to set up is a way to have all of these distros have a common partition for data. I thought I would have a common home partition for all distros but apparently that is not a good idea as it can break stuff.

So, here's what I am hoping to accomplish:
I want a common boot partition for all distros. I'm guessing about 400mb should be enough.
150mb for the efi partition.
I will install the root of each distro in a separate partition, which will be kept as small as possible, but will have healthy room for updates.
Then I will have a large partition for common data.
(I want the root and data partitions to be using LVM)

Also, I have a 120gb ssd lying around that I can add to this build. I am guessing that I can easily create logical volumes that can exist across the physical discs. My question here is that, if the 120gb drive has a part of a logical volume, and it is not available during boot(only the part on the 500gb drive is present), will I be able to use my PC without data loss?

I am looking for suggestions regarding how big I should keep the root of each distro. Please tell me the sizes I should keep for physical volumes and logical volumes. I am not too well versed with lvms.