Two very similar methods for quick overshoot/overlap and settle using maya.

One by Paul Creamer

The other method by Brian Horgan

Remember, scrub your timeline, to the inbetween frame on linear, middle click and drag to the new time, add keyframe. Once done just offset by group of parts.

Also there are a few scripts available to do this automatically.

Overlapper $20 US

https://dkolpakov.gumroad.com/l/Overlapper

Brodynamics $99 US
https://brotools.tech/

Overlappy (Free)

https://www.highend3d.com/maya/script/overlappy-for-maya-105076

Luismi Herrera LMSPRING (Free)

https://luismiherrera.gumroad.com/l/LMspring

LMSPRING Demo