The popular keyboard styles right hand often plays both chord tones (or a chord tone) in the lower/thumb side, and changing melody notes with the little finger side - both at the same time.

Working up the ability to play like this is a step-change in the popular-styles pianist's skill and playing.

Here is a brief video introduction.

Here is Hanon Exercises 1 to 9 with held thumbs. Four varieties are offered - watch the red highlight box down the left-hand side of the video frame.

Because of its particular shape, there is no held-thumbs variation for Exercise 4.