Cross-training in multiple martial arts?

In response to one of my posts from 2007, Jiu-jitsu is Adaptable, an Anonymous commenter posted a couple of interesting and essay-length comments meditating on the merits and practicalities of many techniques vs few, and of different systems of martial arts, contrasting and comparing his experience of Jiu-jitsu with various other styles, including Krav Maga, Kali and Kick-boxing, and finishing up with the question:

What do you think about cross-training and how do you train defenses against kickboxers and armed attackers?

A few comments, broken across a few posts

Cross-training

Can be good, can be bad.  I appreciate that the hope is that by training in multiple arts you will be able to compensate for weaknesses in one art with the strength of the others, but I think that it is more complex than that.  Do you have time to train sufficiently in both arts to really get them? Do they blend harmoniously, or do they contain opposing principles and strategies?

I have students with a background in other martial arts come and train with me.  Inevitably they have a lot of patterns of movement drilled in that are difficult to modify; the level of difficulty varies with the individual and the kind of training that they have done.  Put their body in a particular position or situation and the drilled responses come out.  With those who empty their cups, and persist until they reach higher grades, there seems to be a process of unlearning, and then eventual re-integration, but it takes dedication and time.

Our organization primarily teaches Jiu-jitsu, classical judo and chinese boxing, with secondary arts including (but not limited to) ken-jitsu, aiki-jiu-jitsu, judo-do, and sambo.  So you could say we have built-in cross-training.

The head of our organization replaced his late master's preferred striking art -- shotokan karate -- with hung kuen chinese boxing, because he found that it made for a more consistent mix.  Even masters disagree on these things.

My rough advice to people who are aiming to be in martial arts for the long term is:

1. Seek the best instruction you can find that seems like a good fit for you.
2. If this includes integrated cross-training, great.
3. If not, defer cross-training until you have reached a significant level of expertise in a base art, and then seek cross-training in consultation with your instructor.

I just don't see people without expertise being able to mix and match disparate martial arts training particularly effectively.

Another point of caution is that standards of safety in training vary widely.