We split the cost of an ecommerce site package, but have decided not to be partners.
You may think it's silly to "pay the people twice," but you would be engaging in copyright infringement if you don't. Either buy another software package (and both of you can split that cost, assuming you split the cost of the first one), or see if there might be a less expensive option of getting an additional license associated with the software.
But in the latter case, you would want to have an agreement between the two partners as to how you are disposing of the assets of the business (including the software). Otherwise, you run the risk that if your relationship cools, you will start to fight over assets.