Trying to crossfade text

Long and short: No, simply because you cannot change the source text selectively in such a manner. Rick has already given the longwinded answer - you can create some sort of transition by manipulating the source text and using text animators to disguise the changes with fancy motion, but ultimately it's way more complicated than just creating two text layers.

Mylenium

After Effects is one footage item per Layer.

If you jump over to Premiere Pro, you can crossfade Graphics that contain Text Objects in the same Video Track.

You can keyframe Source Text, but the characters will change from one letter to the next in one frame. There is no built-in transition.

You animate one letter at a time or even one word at a time by setting Source Text keyframes. Then you could add an Opacity text animator and adjust the start and end property to make one letter at a time fade out, then the new letter or word fade-in in, offsetting the keyframes. It will take a lot of keyframes and some careful placement of the keyframes, and you will end up with one letter or word fading out and a new one fading in at a time.

I almost try and keyframe the Source Text property. There are times that I will use an expression to drive the source text, but setting keyframes for Source Text is not an effective workflow unless you want a letter or word to change in one frame. If you use two text layers instead of just one, any transition between two different phrases will be less work.