In Flat rate shipping it does not matter that what is the weight
or size of your box, there is flat rate for shipment with in your
country.
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You can indeed find a flat rate for corporate movers. Research
the company you are trying to do business with and their flat rate
should be on their website.
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It would be at the discretion of the shipper. Flat rate could be
either USPS, UPS, Fed-Ex or whatever method of shipping is chosen
by the shipper for a "Flat Rate". Also, USPS has flat rate boxes
and envelopes.