Is it permissible to be a W-2 paid employee providing software training and support, but have a contract between my employer and my referral/sales commission-based company (which by the way has contracts with other companies) to have sales/referral commissions of the software paid to my company (1099)?

Yes it's possible. However, although you didn't ask about possible conflicts of interest I must point out that this arrangement could be abused in a way that could get you fired. As an employee you must have no authority or influence whatsoever with your employer over the selection of your side company to provide services.