Can I rent from my LLC in 2-Flat? + Get 2 hard money loans?

[Brian H.]

I realize a lot of folks have posted this question, but it seems they're all for SFH's or for tax benefits that I'm not concerned with currently.

I live in an apartment on the south side of Chicago (2 bed 1 bath) and the 2-flat (2 units of 2 bed, 1 bath) one house down from me just came up for sale at a good price. I know the area well, know who's around, etc. and am thinking if I can find a way to finance this through my existing LLC that I'm currently doing a rehab on a separate SFH down the street with, it might make a lot of sense. I would rent one unit to myself, and then rent out the other to a regular tenant. This way my rent would be going towards my LLC owning a property, instead of to the landlord owning theirs. Is there something I'm missing there or a reason that wouldn't work?
The challenge for me, I think would be the financing. I already have one project going and was planning to do hard money to finish the construction, so I'd need another loan to purchase this one. I think I may be able to raise the capital to cover the downpayment and holding costs, but could I get another loan? I had been thinking to get hard money to acquire and do light fix up (it's in decent shape), and then refinance after getting myself and another renter in to season for 6-12 months. Or I could just get a purchase hard money straight out and manage the small fixes myself. Am I stretching?