Yes, it is possible. You need to create a new message with the severity you need (Setup -> Message Pool -> Message Pool). In my super template that I install on every machine, I've created several message levels for "process down". Then, in your process profile you need to create an override message for the correct token (Profile->Messages -> Message override list -> new). For example, if you want message when it goes down, you select your custom message and assign it to token "process_down".
I also do the same with other probes: cdm, ntservices, etc.
Now that I have all those custom messages there, it makes it easier to have "application" templates which can then give proper severities to their components. For example, I can have ntservices in the basic template put all running services to raise an alarm with "minor" severity on a server. Then I push Exchange template on to the machine, and it just configures an override for Exchange services so that they use message "UnexpectedCritical" instead of "UnexpectedMinor" when it is in an unexpected state.
-jon