Here is a list of shows you can crossover with and the story

RWBY: Landing At the snowy planes of atlas in your mech. You enter a unconscious sleep. Soon you wake up to a group of people looking at your mech with other mech much smaller than your. After a intense battle with a Grimm you talks to general iron world about this world you landed in and then yours. You give Iron wood your service rifle and blueprints to the base mech. This is the events between Volume 0 (aka the trailers) and volume 1 then continues to 

RVB: After and intense solo space battle against the Shadowscythes you soon get hit by the strongest one there and land a ring planet and is sent to bloodglutch outpost number 1 during the events of Nobody Likes You.

My hero academia: Fighting a battle against a skilled Shadowscythes you fall at a planet with weird anomalies this takes place at the beginning of the anime.

SCP: Battling a Shadowscythe on the ground you are sent through a portal to the SCP world. you are labeled as SCP-6000 and tested on. Since you are a human with miltary skills. 05 allows you to join taskforce Umbra-0 with your mech(which is SCP-6000-1 to contain Anomalies)