I've worked with clients in your situation & typically have been able to negotiate a 30-40 day seller rent back after close of escrow. This approach has allowed my clients to move just once as well as have a clear idea of budget once their property is in contract with a buyer.
As mentioned, if the subject purchase property does not have a multiple offer situation you may be able to write your offer subject to sale of your property; a seller will be more reassured & your offer will be stronger if your buyer has already removed inspection & appraisal contingencies.
Alternately, I've recently negotiated for a client a rent back prior to close of escrow of the property they are purchasing (they needed more time for finance purposes & all inspections/price negotiations had been completed).
The outcome of negotiations will really vary depending on the needs of buyer & seller. By being creative a win-win can be created for everyone.
If you haven't done so already, you will want to determine your finance options for the larger property as well as pricing & inventory for a bigger home.
Cheryl Bower, Realtor , CRS, GRI, ABR, ePro
Certified Residential Specialist, Graduate Realtor Institute, Accredited Buyerâ€™s Rep
DRE #: 01505551