Modal interchange
Dorian sits near the center of mode-space, and so it has a lot of neighboring scales that are 1 alteration away. Dorian’s a pretty stable mode, which makes modal interchange easy, in both directions, brighter and darker. There are far too many options to cover all at once, so in this lesson I’m going to talk about the options I've found most common and useful.
The Mixolydian I7 landing
♮3 -> Mixolydian
Sometimes a Dorian tune will land on the I7 - the Mixolydian tonic! It's a very characteristic type of lift.
The Soft Dominant
♮7 -> Melodic Minor
When you use V7 in Dorian, you should first notice that it doesn't have the same bite as borrowing a V7 from Aeolian. And the reason for this is basically what mode the V7 is being borrowed from. From Aeolian, V7 comes from Harmonic Minor; from Dorian, it comes from Melodic Minor. In both cases, the borrowed note is a ♮7.
To my ear, this V7 chord has a bright rock/blues sound. Keep in mind that a 12-bar blues has both a IV7 and a V7, and so does Melodic Minor. So it's common to see the V7 alongside IV7 chords.
This also gives you a classic functional turnaround: ii7 - V7 - i7.
The Aeolian dramatic turn
♭6 -> Aeolian (natural minor)
It's actually pretty uncommon to hear a ♭6 borrowed from Aeolian in the melody over a Dorian section - but it's really common to hear a whole chord being borrowed, most commonly the ♭VImaj7 (and sometimes its darker sibling, the Aeolian iv7). It's crazy useful.
One place you'll see this often is when you launch from a Dorian A section (maybe a i7-IV7 vamp, for instance) to an Aeolian B section. And very often you'll see a ♭VII right after it, for an Andalusian Cadence (♭VImaj7 - ♭VII - i7). You'll learn more about the Andalusian cadence in the Aeolian lesson.
Another really common pattern is i7 - ♭VII - v7♭5 - ♭VI.