Yes! This is something I've been working on - not for the sake of the M2 mode itself (head voice / falsetto), but because M2 development tends to help with high notes in M1. When I started studying with my current teacher, my M2 felt somewhere between absent or very weak.

Typically exercises I work on for M2 start with an SOVT (typically straw phonation, puffy cheeks, or water bubbles) and then transitioning to an [u] vowel on a five note descending scale. For me, at least, while this can be very unstable depending on the day, M2 is much more easily accessible with an SOVT.

You might also start with a gentle SOVT in M1/chest and siren up as high as is comfortable without pushing/pressing or trying to be loud. Don't think about registration, just let it go - SOVTs tend to let the voice go where it wants easily.

Highly recommend my teacher's book: https://www.pluralpublishing.com/publications/a-systematic-a...