Assuming they can increase cost of delivery (something that, apparently, congress is against), chances are this is what would happen: they raise prices to cover (marginal) costs, and some customers run away. A commercial company would reply by either cost-cutting, shutting down (parts of) the company, increasing productivity, or finding new revenue streams.

The USPS does not have first or second options, and the third on its own only helps if it brings in extra work, which it does not (remember the 'some customers ran away' part?)

It all boils down to the fact that the USPS is not operating in a free market. They have huge expenditures that they cannot get rid of. If you have an employee, but no work for him, and cannot fire him, it makes economic sense to take on work that pays less than what the employee costs. Sure, it loses you money, but it loses you less money than not taking on that work.

So, that leaves the fourth stream. In e EU, that has seen post offices turned into shops, selling mail-related stuff such as postcards. That may work, but especially in smaller villages, it is easier to outsource the post office tasks to existing shops, rather than trying to compete with them in a market that cannot sustain two shops.