Yes, IMHO, it is possible to train in more than one style at a time. Usually, the first concern that comes up is, "How do you find the time?" Well, sure, that can be an issue. Most of us work 40hrs a week, sometimes more, and there are only so many classes a week and only so much time you can devote, so....
Now, while everyones goals will vary, I do it not for the rank, but for the sake of learning and expanding my knowledge. After around 10yrs, on and off, due to my work schedule, I tested last month for my Black Belt in Arnis. I tested with 3 others who also have many years in, but never tested on a regular basis. Was that a concern for me, that it took that long? Not really, because as I said, I'm not chasing rank.
Another concern is "Can you be effective if you're only training in something 1 or 2 times a week?" IMO, yes. Sure, you progress at a slower pace, but again, what are your goals? To learn an art or to test every month so you can have a new belt to hang on the wall? Of course, supplementing those classes with privates and informal workouts is also a big plus.
I do feel that you should have a base art first, before taking something else on. Myself, Kenpo is my base, and I didn't cross train until I was Brown. The 3 arts..Kenpo, Arnis and BJJ blend very well.