Cross training I would recommend would focus on mindset, intention and functionality, creating a more well-rounded fighter for a street scenario
Running short distances, sprints, and working on “bursting” (transitioning to a high level of speed quickly) is very efficient for Krav Maga if you have to get away or improve your position. It also builds your cardio and stamina. I also suggest going up stairs or uphill running.
HIIT training (high intensity interval training) like Tabata, where you do short bursts of high intensity work outs, with very quick breaks. It’s good for cardio, strength and stamina, as well as mindset to keep going even when it’s hard, without slowing down.
Pilates is great for strength and body awareness.
Jumping rope is good for cardio and timing and bursts of legs so you can kick faster.
Ballet and salsa and waltz are also great for improving cardio and coordination.
Yoga is excellent for mobility and flexibility and body awareness. I am a yoga practitioner (see a picture of myself and my teacher Rebecca Hajek) and just got certified as a instructor so I wanted to add a bit of an explanation here. Make sure you have a good teacher. Some teachers do not put emphasis on technique and form, which can get students hurt if they don’t know what they are doing.