Can a taxpayer's s corp pay their sole proprietorship company?

You will need to clarify.  You have an S-corp, and you want to hire yourself in a different capacity?

I don't see a tax advantage, for one thing.  The S-corp will pay the gross and not have to withhold taxes, but the sole prop will have to pay income and SE tax.  If you are thinking your sole prop can deduct expenses, those expenses are probably also deductible to the S-corp.  And remember two rules (and think about how they work together here):

1. All compensation an employee provides to an employer must be reported as wages and included on the employee's W-2 and subject to all tax withholding, unemployment insurance, and so on.  Employers are not allowed to hire an employee but provide a bonus or some of their compensation separately on a 1099.

2. The owner of an S-corp must pay themselves a fair salary as compensation for work performed for the S-corp, and those wages are subject to all employment taxes, before the S-corp can distribute profits that are not subject to medicare and social security. 

I don't see how you can follow those rules and pay yourself for separate work on a 1099.  Smells fishy. 

doing so and conforming to tax law would likely cost you some additional taxes. The S-Corp needs to pay you a reasonable salary. the rest of the income is subject to income taxes but not self-employment taxes. paying your sole proprietorship would increase its income by the same amount it lowers the S-corp income so there would be no change in your personal taxable income. however, now the sole proprietorship would be subject to self-employment tax on that payment.  possibly even worse is if there is no valid reason for the payment the IRS would disallow the deduction to the S-Corp. how they would treat the payment on the sole proprietorship side is unknown.