The highest cash out LTV's are from Fannie/Freddie, which both cap it to 75% for 2-4 unit owner occupied properties (70% LTV for non-owner). Conventional interest rates are also higher than FHA's, assuming the same exact scenario. With FHA there isn't any hit to the rate for cash out or multi-unit properties, but with conventional financing there are hits to the rate for both. That is why you are having a tough time finding what you are looking for with conventional.
You should look into the Fannie Mae HomeStyle renovation loan program, which is conventional financing for the sole purpose of renovations. The program will go up to 75% LTV on 2-4 unit properties. The calculation for the LTV requires a worksheet to be completed, which you can find at https://www.fanniemae.com/content/guide_form/1035.pdf. With this type of loan you need to hire a general contractor who will be reviewed/approved by the lender and will be in charge of the renovations.
If neither of those appeal to you, then FHA financing will do cash out to 85% LTV on a 1-4 unit primary residence.