I'm not a doctor and I don't live with you so I don't know what exacly you eat and how long you have been eating this low but I really doubt you would experience refeeding syndrome under your bmr if your usual intake is 500-600 cals, I don't know much about refeeding syndrome so make some research about this subject if it worries you. Also 900 calories is still low restricting in my opinion.

 

For most people 800-900 is probably medium restriction. You have the right idea about doing it in steps, but at the end of the day, if you feel like you can raise it a bit faster than you intended, it will be fine too. I really doubt you could trigger refeeding syndrome but also you didn't state how much you weigh etc currently. It's not that big of a change really to have a 300 kcal increase, many regular snacks can be that much. And reminder that if you see any increases on the scale its definitely just food or water and will stabilise and you will lose anyway at that.

 

I am currently in the process of doing exactly this but to increase my maintenance.

I have increased 100 calories per day per week every week.

Week 1: 1000 per day
Week 2: 1100 per day
Etc.

Go until you've reached whatever your goal is. My goal is that I need to fix my maintenance to keep losing, but you can do it however long you think you need. I am up to 1400 and I've lost, but 1400 is fucking miserable and idk how I'm going to keep going. I have to keep going to 1800 because that's where my maintenance should really be...so, theoretically I shouldn't gain and 4 weeks in I haven't found that to be the case so your idea is solid as far as my experience goes.

 

800-900 is actually low-mid restriction for just about anyone

 

That's not a huge jump. 800 is my base so some days I'm down lower. I mean it's not like I'm at 600 all the time, but I think you'll be fine. If you are worried I'd say kick it up 25 every couple day, see how your body reacts, then another 25. Keep going a couple days at a time until you're at where you want to be. It'll probably be less scary that way too because you'll only add a food here and there instead of a whole meal. When you're at your new calorie count you can readjust your meal plan to accommodate and plan new meals and snacks.

 

I did something similar a few months back, was on roughly the same amount you’re eating. I increased by about 100 a day, every few days. Tbh I actually felt a lot better for it, and increased it more still, and was maintaining on that (I’m currently gaining a little through choice).