Greens mustn’t interfere with hay eating, so don’t give too much. 2-3 cups is ok imo. I think I gave my bunny Bam double that amount and he actually got fat from it – even though it was mostly fresh foraged leaves like dandelion and apple and yarrow and plantain etc.
Fresh grass is fine though (start with smallish amounts as with any new veg). Fresh grass works like hay, it wears the teeth and it has lots of good fiber. When my vet put my Bam on a diet he was to eat grass or hay, 1,5 tbsp pellets (the amount varies depending on type of pellets – Oxbow type pellets weigh about double per volume than extruded pellets) and just a small salad in the evening. This diet was VERY effective. And I dont think my bun felt deprived, because from his behavior, I think it’s safe to say bunnies find fresh grass super yummy. Just make sure it’s not treated with pesticides or picked in a place where raccoons poop.
The problem with fresh veg is that it’s yummier than hay, so if the bun gets too much, hay consumption suffers. Hay consumption can also be a bit difficult to measure since buns must have access to hay 24/7.
As a person that has caused a bun to get fat on greens, I like to recommend weekly weighing. Keep a weight diary, there’s no need fret about 20 grams here or there, it’s the long run that counts. A weight diary can also help you spot un-intended weight loss, which can be an early sign that something isn’t right with the bun. It’s difficult to assess a bun’s weight loss or – gain with the eyes only, unless it’s dramatic, because buns are so fluffy.