Cross-training martial arts means adding a second art to the one you already practice. Before I ever stepped on a jiu-jitsu mat, I trained aikido for several years in Moscow, Gomel and North Carolina, and Krav Maga for several years in Los Angeles and Dallas. Both arts left something in the way I grapple today.
How I ended up in Krav Maga
I started Krav Maga because of a movie. I liked The Bourne Identity, looked up what martial art the main character used, and what I found pointed to Krav Maga. So I found Krav Maga Worldwide in Los Angeles and started training there. When we moved to Dallas, I kept going and reached orange belt.
Years later I found out there had been a Machado jiu-jitsu academy close to where we lived in Los Angeles. Eddie Bravo started jiu-jitsu at the Machado brothers' academy in April 1996, and he later got his black belt from Jean Jacques Machado. As I remember it, Joe Rogan trained there too. I had no idea at the time, and once I started BJJ, I regretted it.
What Krav Maga taught me: the free hand
Krav Maga is built around the street, where the goal is to survive at any cost. BJJ leans more toward sport. I carried the street idea with me onto the jiu-jitsu mat.
When I roll, I always know that if my opponent has a free hand, that hand could hit me. Because of that, I skip some techniques I could otherwise use in BJJ, and I pick the ones that keep me better covered against a strike.
The clearest example is bottom side control. The moment I end up there, I work to hide my head from an imagined punch. If I ignored the real-world danger, I could lie there relaxed and work the classic BJJ escapes.
What aikido taught me: go around the force
Aikido gave me my breakfalls, which I wrote about in Ukemi for BJJ Players. The bigger lesson was a principle: everything moves in circles. When someone pushes into me, I look for the angle around their force and let the head-on collision pass by.
That helped me in judo, especially with kuzushi. Neil Ohlenkamp explains kuzushi on judoinfo as breaking balance, and thinking in circles helped me understand it. It helps in BJJ too. In my BJJ classes nobody spelled this idea out. I got there on my own, because of the years I had spent in aikido.
Two ways to cross-train
Many people who train BJJ also train Muay Thai. That is one way to cross-train: add the striking art next to the grappling one.
My way was to switch for a while. When I reached brown belt in BJJ, I realised my top game was missing. So I deliberately stopped BJJ and switched to judo. I trained judo for two and a half years, earned my judo brown belt, and came back to jiu-jitsu. I wrote about that switch in Judo for BJJ Players.
The order I would recommend
If you are choosing where to start, I would start with Krav Maga, because it is the most practical for self-defense. After Krav Maga, I would start BJJ. Krav Maga has a section on defending yourself on the ground, and it only really opens up once you train jiu-jitsu.
The same thing happens inside BJJ. The takedowns and the standing game only open up once you have trained judo well and know how to behave on your feet.
Whatever second art you add, write down what carries over from one mat to the other. A BJJ training journal has room for both.