Can one keep applications on an SSD drive

Some applications will apply their updates on the boot drive regardless if the previous application version is on an external drive, and other applications may fail to apply an update because the expected application is not found on the boot drive.

I agree with Luis Sequeira1 that you should find other storage hogs that you have downloaded or Mail messages with large attachments rather than introduce other potential issues by moving applications to an external drive.

I agree with both the Previous Contributors

This kind of smacks of ( Running Application from External Drive ) like a Microsoft Windows thinking

Yes, MS Windows may allow some applications be installed and run from an External Drive

Yes, MS Windows may also allow the External Drive to be used as additional RAM

But macOS expects most application to be on the Internal Drive for the reasons already presented by others

Some applications can be run from external drives, but if you are low on space, there are probably better ways to make space than by moving applications.