Is your co-op your primary residence? If not, it’s going to be very difficult to get cash out. There are lenders, but the rates will be high. If your coop is your primary, your only option may be to refinance your first mortgage and take cash out. A 2nd mortgage on a coop is difficult to obtain because there is no collateral to hold (the first bank is holding the stock and lease and there is only one of them as opposed to real property where the lender receives a deed of trust). If you really want to go with a home equity, the only lender that may consider it would be the lender that owns your first mortgage since they already have the collateral. I’d check with them to see if they would do a home equity on a coop, but if not your only option would be to take cash out, which I don’t think is a bad option. Rates are low now and closing costs on a coop are usually pretty cheap (around $3,500). Feel free to PM me if you want to talk more specifics.
That being said, it comes down to the numbers. If the property is positive cash flow not only in its ability to cover its own mortgage, but to cover the difference in additional payment from your cash out refinance on your primary and then some it’s a win win. It’s all about finding the right opportunity.