How can you house hack a MF and still hold it under an LLC?

[Robert E. Medlock II]

Hello BP community. I have been racking my brain for the past few weeks trying to understand how NOT to violate the "Due on Sale" clause.

Here's the scenario: Jane wants to buy a 4-plex. However, as a new investor of multi-family properties, she can "invest" sooner and much easier as an owner-occupant. After purchase, Jane would also like to move out of this 4-plex ASAP to realize it's full cashflow in her growing portfolio. The question that has now arisen is how can she purchase as an owner/occupant AND then hold the property under her current LLC without triggering a possible due on sale clause from a quit claim transaction? 

Any insight on how this can masterfully be done with surgeon's precision would be greatly appreciated. Likewise, if possible, to what degree can this be duplicated?