If your credit is marginal enough that a credit inquiry makes a difference, you shouldnt be buying a house.

Many fewer MF properties as compared to SF by a large margin.

This cuts the margins I was thinking I’d get or requires me to offer lower. 

Slim profit margin, any repairs costs have you going negative, upcoming vacancy costs will have you coming out of pocket, and the asset isn't appreciating in a way that will generate profit.

I would suggest putting in applications to several banks at the same time, this could affect your credit score by a small margin due to the hard inquiries, but you should be able to get approved for all of them at the same time.  

The outcome shows that EquityBuild, in its enthusiasm for Chicago apartments, overpaid for the buildings, and by a wide margin: Four buyers have agreed to pay a combined $7.7 million for properties, about 33 percent less than the $11.5 million EquityBuild paid for them over the past few years, according to a court document.Yet the combined price is slightly higher than the $7.4 million that the properties were listed for.

The margins on oil are about 60 cents a gallon .

By not putting 20-25% down it is causing you to run extremely tight margins, which in turn could put you in the red when faced with a multiple unit issue.

Debated taking the risk of making some improvements while I'm in it....flooring, paint, etc. and trying to house hack it, but didn't think the margin was there.  

I would not personally want to leverage this property much more as the margins will get pretty tight.