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Question: My iron won't go up even though I'm supplementing
The top things that I would think of would be riboflavin and copper, plus inhibitors of iron absorption. So generally speaking, plant foods are strong iron absorption inhibitors. Generally, you're going to have organic acids that promote iron absorption in proportion to the amount of potassium in the vegetables that you eat, although it's also the case that polyphenols will tend to correlate. And polyphenols inhibit iron absorption, so I'm of the opinion that you shouldn't eat plant foods at the meal that you're trying to get your iron in if you have trouble getting your iron up.
I would take the iron supplement with a carnivore meal. If you want to eat plant foods, eat them at some other point in the day.
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DISCLAIMER: I have a PhD in Nutritional Sciences and my expertise is in performing and evaluating nutritional research. I am not a medical doctor and nothing herein is medical advice.