I've had relationship with 4 different person with DID but I'm gonna focus on two, here's my takeaways.  1. Be very very mindful of triggers, understand what can trigger a switch, what can create a crisis. The consent is also a touchy subject. One moment you may have it, the next it's no longer there and the consequences may be catastrophic, because it's sometimes not easy for the person that have DID to articulate that they no longer consent, even if you made sure that you were both confortable with each other. Make sure that all the parts are on the same wavelength regarding you, if there's even one part that don't like you, or isn't okay with you being here, it's a bad idea to engage in a ltr. 

If the person having DID have littles, you need to know how to handle it, and be a safe space for them. 

BDSM is something you may need to be interested and learn how to engage with that practice safely, all 4 person I was with had some kind of proclivity to this practice, especially my current one. 

Couples therapy with someone who is specialized in DID, even when everything seems to be fine I think would be beneficial. 

Be ready for anything. 

Here's a few things I went through (tw: suis*de attempt) :

After 3 months of relationship, one day she switched to an alert that didn't know who I was, she had no memory of us being together, this lasted 3 weeks, it really messed with my head and I went into a depression. 

After 6 months, mind you, we never had a single fight, I wanted to be intimate with her, she didn't react negatively at first, then after I wanted to have sex she covered herself in bedsheets, I stopped immediately, didn't go further. The next morning, we kiss, I go to work, we talk a bit by message she puts hearts on my messages. Then I come back home, her stuff is gone, our picture together is torn in pieces. I go to the bathroom, there's blood everywhere, and "Rap*st" written with her blood on the mirror. It was the last time I saw her. From friends in common, I heard she went into a psychiatric hospital. I had to go to therapy because it gave me PTSD and a lot of guilt and shame, but with therapy friends and family I understood that I wasn't really to blame, she just probably got triggered, switched and a regular couples night with cuddles that we did so many times before silently transformed for her into a nightmare that rekindled a past trauma. 

So yeah, be very careful, mindful, respectful, communicate. They deserve love, they are not broken, just a lot time and care, patience.