You will want to explore the category of loans called "non-QM". The most popular in this group is DSCR (debt service coverage ratio) where you qualify on the property itself rather than your personal income, taxes, DTI, etc. It is popular amongst investors because you don't get capped at a certain amount of products, it requires less paperwork, and it doesn't look at DTI/taxes/income.
However, there are other loan types in this category as well such as Bank Statement Loans, P&L Loans, Asset Based Loans, etc.
Generally speaking you will be able to get 80% LTV on a cash out refi (as long as credit is decent and property doesn't have any super unique qualities). You will also want to take seasoning into mind. Different loans have different seasoning periods - so you'll want a nonQM loan with low or no seasoning and that will still allow you to use the higher of the new appraised value vs the original purchase price.