Teaming is quite common in business. Companies find themselves competing on some programs and teaming on others.
Synergism is paramount in teaming with any size company, whether in a lead or subcontracting role. There should be technical, management and market segment similarities between you and any company with whom you are considering teaming.
Your prospective team member ideally will not be a direct competitor; rather a business in a related field with whom you share a mutual need for each other's contributions in pursuing large-scale projects.
Relationships must be developed with primes and other small businesses that can help you, team with you and keep you in mind as they search for success. That takes time, patience and open-minded, out of the box thinking.
It also takes more than a Non-Disclosure Agreement (NDA), a teaming agreement (TA) and a proposal to succeed. It takes dynamic marketing and communication with strong partners and hard, innovative work. Nice buzz words you say - but it is the truth and you have to find what that truth means to you.
See the below free articles on how to develop teaming relationships, protect your interests and your intellectual property.
Small Business Teaming
Protecting Intellectual Property And Proprietary Data