In general it is not possible to install applications on external drives. The data can go anywhere but applications, primarily ones such as Adobe has where there can be parts all over the place should remain on the hard drive.
Either move lots of data to external drives or get yourself a new internal drive.
FWIW, I have essentially all of my data on an external drive (and I have a 2nd external drive to back up the 1st drive), I also use a cloud backup service incase of disaster.
In the Adobe Creative Cloud application, click on the "settings" icon (the gear shaped thingy near the top). Then click on "Apps". There you have an option to specify where the applications will be installed. Please note: because all applications modify the registry file, which is on your system (C:) disk, you will not be able to launch any application from an external drive if you plug it into a different computer.