Depending on your deployment tool I would suggest you replace the cached transform with an updated and then perform a reinstall.

AngelD is assuming, I believe, that your original deployment was with a transform also, but that's not what I read from your posting.

Assuming I am right, and you don't have an existing transform deployed with your application, then I know of no way to apply the transform to your existing installation without actually performing a re-install with re-cache.

Are there any operational reasons for not wanting to implement a re-install?

 So you want to change something after you've installed.  And you don't want to uninstall.  I'm pretty sure that's called a patch :)

If you already have the new .mst, just combine it into the MSI (you can use ORCA or a vbs from Microsoft to combine the changes of the .mst into your .msi) and then run the updated .msi through the Wise Patch Creation tool to make an .msp that you can send out.

What happens if the new transform changes something that was originally changed in the first transform? When you patch the original MSI, will this override the setting of the original cached MST during a future repair?

I do think we need a clarification regarding if the "first" installed used a transform or not.

Should a transform have been used during initial install and a patch is used to update any MSI information then there could be a "conflict" between the already-used-transform and the patch transform(s) used during patch. The best way to find out is to updating a copy of the original MSI and then "apply" the transform (in ex. InstEd/ORCA), this should give you some indicattion if a possible "confict" will occur.

The patch will not update the cached transform, only the cached msi in the form of patch transform(s).
A possible repair shouldn't have any impact as during a repair the msi + transform + "patch" transform(s) will be used (in that order).

I think we have bottomed out all the possible risks depending on whether you have used a transform with the first install or not, so at this point, it's up to you to determine the way forward.
Whatever your solution, test the install, the update, a repair and an uninstall thoroughly.