Root progression by descending third like
I vi IV ii is a standard thing in classical and pop music. I think you should not consider it a retrogression. Technically harmonic retrogression means not following the functional flow of pre-dominant, dominant, tonic. The descending thirds progression is all pre-dominant in that sense. If it continues to a dominant, it isn't retrogression.
A secondary dominant is common:
I V7/IV IV like
C C7 F.
I iii IV or
I III IV (minor or major mediant chord) are used.
I V IV I is a retrogression ...but it's still an option. It can work for blues/rock/pop.
You could also try some modal flavoring. Like mixolydian:
I bVII IV.
If you haven't ruled out mode changes on
IV themselves, try
I iv I for the borrowed chord feel or
i IV i for a Dorian feel.
Try diminished seventh chords: an
E diminished seventh before the
F, or a common tone diminished seventh which would be an
F diminished seventh before
Of course you can try a variety of
You will need to work out the specifics of voicings, harmonic rhythm, surround harmony, etc. to get things to work.
I'm not sure if you mean to only consider
I IV, but it seems worth mentioning that
I IV I or
IV I can often work as an embellishment of the tonic chord, or it's sometimes called a tonic prolongation. That may sound like classical harmony hair-splitting, but I think
I IV I in rock music often works exactly as a tonic embellishment.
Contrast that with
IV acting like a pre-dominant.
I IV ii V,
I IV V, etc. basically anything where
IV doesn't go to
I but some other goal.
IV sounds more "assertive" in that "functional" role.
I think when trying the possibilities for how to incorporate
IV it's good to keep in mind that embellishing versus functional distinction.