Not that I know of, you can only add that trigger for specific parameters.
Probably the best workflow for that would be to set up the updater for that specific parameter trigger not find out afterwards what triggered it. Two distinct execute methods for two distinct parameter changes, from that point onwards same underlying code logic. You can add multiple parameter triggers but can only respond to their current values i.e. you would have an idea which parameters you are monitoring so know which ones to review.
If you've used ChangeTypeAny to monitor all changes of parameters then the updater data method noted previously will likely only report that change type.
In the end updaters should be very finite in their scope, otherwise they get into a mess of self triggering. Seems awkward but it is awkward for a reason i.e. to get the developer to properly scope what changes they are monitoring.
What would be the aim in needing to know what parameter changed out of the ones you are monitoring? You respond to the whole picture don't you?
