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Much like diatonic harmony has its common movements and progressions (I, IV, V,...ii, V, I.....I, vi, IV, V....etc), non-diatonic harmony is also much more likely to be used in certain ways.
Non-diatonic harmony isn't just a free for all, requiring instant shifting from one tonal centre to another in a completely unrelated way. At least, not when it's done well it isn't!!
One of my favourite pieces of advice was given to me during a guitar lesson with Nick Johnston, and he put it as "When it comes to guitar playing, you are what you eat". What he was getting at is that we as players are unavoidably influenced by whatever we listen to, so if you're trying to learn gypsy jazz but spend your days listening to Polyphia then you're working against yourself.
I'll go a little further on this as well, because as a guitar teacher the use of "non-diatonic" here sounds almost like it's being used as a genre and that raises a flag for me. Non-diatonic covers a huge range of stuff, from simple borrowed chords like a minor IV chord or a secondary dominant all the way up to atonal craziness and serialism. By all means, if you're looking for advice on a way to tackle a specific movement or progression then absolutely carry on down the rabbit hole. But asking for advice on "non-diatonic" playing is almost as broad a question as asking for advice on diatonic playing.
Diatonic stuff sounds nicer anyway, that's why keys exist ;-)
So if you move from C Major to Dm, you can use the C Major and then the D Dorian shape (even though it is all C Major notes), it's where the semi tones are in relation to the underlying chord. BUT......
You could also play the C Mixolydian or the C Lydian shapes over the C Major (so implying either a dominant 7 or Major 7 with a b5).
In which case you would in case a) follow with the D Aeolian.
In the C Lydian case following with Dm you are going "out of key" as for Lydian it would normally be followed by a D7, But in this case you could play say the Dm Pentatonic with a slight bend on the F to F#. It gets a bit spicy with the Dom7 of the pentatonic, so either avoid or ascending play the major 7 but descending play Dom7.
The more complex the underlying chord the few choices you have when playing diatonic.