The answer is usually yes.  Most modern suppressors are modular meaning you can swap out different pistons or adapters for various threading and/or caliber.  Keep in mind that shooting a 9mm bullet through a .45 suppressor will not be as effective as a traditional 9mm suppressor.  By design, a .45 caliber suppressor will be built to suppress a .45 bullet.  The smaller diameter, faster travel time, and different bullet weight of a 9mm will affect the suppression.

Older suppressors may not have the ability to adapt different calibers and/or threading.  Your best bet is to check with the manufacturer of each suppressor.  I own an AAC Ti-rant 45 which has different pistons for 9mm and .45 ACP.  I have used it with my USP-SD and it works great. I have also used the Ti-rant 45 with several .22 hosts and it works great. Although I have to switch to subsonic ammo to get a reasonable performance.  It's a much cheaper alternative to buying another 9mm suppressor and waiting another 7 months for the paperwork to come back. The pistons shown below are for use with the Tirant 45.

This same concept also applies to other calibers. Rifle rounds like the 7.62x39 and 5.56 can be fired from the same suppressor. Of course, NEVER try to fire a larger caliber than the suppressor you have. Some shooters with multiple suppressors will mark them accordingly so they do not grab a 5.56 can and accidentally attach it to a weapon shooting 7.62x39.