The process of "applying for a mortgage" means different things to different people.
If you follow the outline here:
Country Home Mortgages - Mortgage Process , it is bascially impossible for two lenders to get to the point that they would both underwrite your mortgage. Once one lender actually enters a credit report that you are BORROWING the amount of loan no other lender will proceed with the process.
If you merely want to PAY two or more lenders to take your application and review through the "processing" step that would probably be a waste.
Far better to determine with as much certainty as possible that ONE of the lenders that you have interviewed can meet your closing deadline. Despite the stories that crop up, MOST loans are ready by closing, especially when the borrower supplies all info in a timely manner, the agreed price is well within the appraisal amount and no flags come up on credit reports.
Truth be told even if you wanted to pay two or more lenders to process your loan application it is likely that the cross checking that many lenders do would raise a flag that you are trying to pull a fast one.
I would strongly suggest you instead get as much assurance as possible from as high up the chain as you can that your loan will be prepared in a timely manner...