Theoretically it can be possible, but only on a case by case basis, ie. it might work for some applications, while it won't work for others.

It has a chance to work only if exactly the same application package version is used in both distributions. Then you can try the following:

1. install the application in your "primary" distribution


2. check which files are contained in the package (you can do it with dpkg-query -L packagename)


3. on the other distribution, create symbolic links in place of all these files, that point to respective files on the mounted partition of the "primary" ditribution


4. optionally, you can similarly create symbolic links for configuration files/folders of that application in your /home/user directory, but this can be tricky, as it is not always easy to know which particular files/folders the application uses to store config.

In my opinion, even if this may work, it's not worth the effort, as you have to do it for every application manually.