Hey mate, yes you can (as you put it) "Cross Train". For me, I do both Brazillian Jujitsu (i've done since 2008 through school and then on/off since 2010) and have been doing Goju-Ryu Karate since 2001 (recently became a Shodan Level Black Belt). And I have found that by doing Jujitsu it has greatly helped my standing fight game along with the groundwork. But for Aikido and karate they can go hand in hand so they work quite well. you will understand both martial arts at a deeper level. But you will want to practice at home for karate.