How to add multiple transitions to the same text animation?

Hi, I'm trying to replicate a text effect used in another of my company's videos where the text has a linear wipe and also fades in, starting with a low opacity and building as the text wipes from left to right, as if it's being written.

I feel like it would be easy enough to replicate by adding both a 'cross dissolve' and 'wipe' transition to the text animation so that they initiate at the same time but this doesn't seem to be something that Premiere lets you do. A friend told me keyframes can achieve a similar effect but my skills with Premiere aren't quite there yet.

Any tips? Figuring out how to have multiple transitions play at the same time would be the easiest solution, but I'm not sure if this is possible.