They may do better with less common ones like duck and venison.
Go offers some helpful options, they have a variety of meats to choose from. Hounds & Gatos have a variety as well.
If you prefer to feed your cat raw food to constipated cats.
With some cats, constipation is made worse by foods with ground bones - most raw recipes have ground bones in them. When that is the case, then you could make homemade raw food with one of these complete supplements.
Please keep in mind that cats can die without enough of certain key nutrients so you need to follow very specific instruction if you want to start a homemade raw diet.
Current Supplement for making homemade cat food:
Alnutrin Supplement: A good supplement and recipe for bone-free homemade cat food. You can request a free sample and they will include the recipe.
Feline Instincts Supplement: They provide a recipe and nutrient supplement, which makes if easy t make - sure your cat gets what they need.