The properties and the loans will most likely need to be in your personal name (no LLCs), and you'd need sufficient credit, income, and DTI to qualifiy for both loans simultaneously. 

If you want to try an advanced statistical technique to improve your chances of increasing your response rate, research Design of Experiments (DOE), which is a multivariate method of testing many factors simultaneously.

And if it is, am I able to sign a new lease and issue a 60 days notice simultaneously?

Find a house in decent shape and focus on the areas that will increase the value and appeal to people simultaneously. 

Simultaneous closings and assignments are your best friend.

--Become a hard money lender somehow--Figure out how to get in on an apartment building somewhere (although I'm currently trying to build a new business and don't have time to simultaneously learn another one).

Or several closings simultaneous to your sale?  

I'm planning to do double or simultaneous closings. 

The residential note field is a field filled with regulatory land mines, attorneys looking for class action lawsuits, and deadbeat borrowers spending 2-4 years living for free while simultaneously destroying the house.  

Hello,I am in the process of beginning to search for a 2-3 flat in Chicago that my wife and I can live in and simultaneously rent out the other unit(s).