I believe one may begin training with others from other systems provided one has a solid base in their core art. A solid base does not mean X number of forms, Y number of techniques, or Z belt ranking (although, knowledge generally follows rank, but we've all seen exeptions to this rule).
A solid base, I believe, is not just the ability to perform, but also being able to have a solid understanding of that core system such that it may serve as a means of dissecting all other systems. This is one of the things I have enjoyed most about AK. Its focus on truly universal principles endows one with an understanding of the fundamentals and mechanics that comprise all systems. The focus of my training is on the kenpo system, not a "style" called kenpo.
I think there is a threshold level to which one can train in another system. If I can integrate the lessons into my current base of knowledge without cannibalizing the fundamentals I have already engrained, then it can be a positive experience. What I don't want to do is let my neutral bow to start changing. I don't want my hands in a mantis position, and I don't want my fists at my temples. I don't want to look like a monkey or a tiger, I don't want to trade back and forth with someone attacking with a knife, and I don't want to practice against unrealistic attacks.
Granted, this approach, will may diminsh one's potential for success in the new system. This is fine, because my core system is still my area of focus. Terms used to describe this approach have been "investigative inquiry", "cross-referencing", and the like.
In general, you cannot start up in another school as a white belt with a solid understanding of your core system without that new instructor wanting to change your basics. Bad idea, I believe. The best approach I have found is to train with other students whose minds are open as your own. Walk in with the disclaimer that you have no intention of changing your system, but want to learn about how they do things and, more importantly, how your system fairs against theirs.
One more thing that's important, we should be up front and honest with our instructors. TELL THEM what you are doing. Share with them your observations, and get their advice. Only an insecure instructor would be offended by your inquiries, and an amaeteur instructor will have no solutions to your questions. My own teacher encourages this if we so desire, because he know we will always come back to what he is teaching, and often you come to the realization that you are spending valuable time in something that does not really benefit you.
One final note, training methods have no boundaries. I occasionally drop into a school to simply watch, because I want to see how they drill, how they condition, how they generate power, what state of mind in which they operate, and how they teach and run their school. I have learned many conditioning drils by watching a local Kyokushin school (the teacher was promoted to 5th dan under Mas Oyama - needless to say he can get the job done, and so can his students). Sometimes I walk out of a school I visit within a short time, other times its worth watching.
Good topic,
Steven Brown
UKF