Hello Mark,
When you say multi unit do you mean 5 or more units? If it's 4 or less here is what you're looking at. Freddie Mac will only allow 4 financed properties max. However Fannie mae will allow up to 10 financed properties but here is how it works. If you have more than 4 financed properties you can only do a cash out refinance refinance if you've had the next property for less than 6 months on financed loan numbers 5 to 10. This called delayed financing. There are other guidelines you need to follow but they're very simple.
So in your case assuming that one of your unit properties are 4 units you could still do a C/O refinance on that home.
On your 5th financed property you could only do a rate and term refinance unless you qualify for delayed financing.
So if you C/O on your unit and buy another home cash and then take 3 months to fix it up and then decide to refinance it C/O that is fine. But if it take 7 months to fix it up then you would have to get a HML. After the HML is completed then you could do a rate and term refinance on that 5th property.
You should have been able to get more LTV unless your DTI was too high.