You will run your business as partnership or LLC, you will avoid double tax. When you open a business account in a bank, you may need a tax identification number or you have to use your social security number.
I think you do not need two tax identification's numbers.
By the way, Partnership is different from LLC. Once you have partnership, you may need some legal products. You can go to to buy partnershp kit. or just visit the web site to see what supplies a partnership needs.