Help! Only approved 70% LTV on Cash Out Refi

[Mike Barry]

New investor here looking for advice from those who might have been in this position before or those who are smarter and wiser in this situation. I am currently attempting a cash out refi on an investment property of mine to not only reduce the interest rate but mainly pull some cash out to use as a down payment on my next investment purchase. I was originally told I can borrow at 75% loan to value by my lender, but after he submitted everything to Fannie/Freddie underwriting it came back I was only approved up to 70% LTV. This is throwing my plans off because I do not have that much equity in the property to pull much out at 70%. I was considering going to another lender to attempt to secure the 75% however my question that I am wondering is if this second lender or any other lender will be restricted to the same Fannie/Freddie guidelines? Will this only delay things and hurt my in the long run having my credit pulled and put through the process only to be told the same 70%? Has anyone been in this situation before?

As of right now I am at least lowering my interest rate by almost 1% so there is still value in me proceeding. However, my ultimate goal is to pull money out so I am not sure at this point on what my best bet would be.

Any and all advice would be very much welcomed! 

Thank you all in advance!