In grammar systems, such as cooperating distributed grammar systems, a team is formed from a finite number of components. In every derivation step, one rule from each component is used to rewrite a symbol of the sentential form, hence rewriting is done in parallel. Several derivation modes are considered, varying from using a team exactly one time to using it as long as possible. The possibility of different teams having different modes of derivation is defined too. The power of all such mechanisms is investigated exhaustively and in many cases the forming of teams enlarges the generative power of the underlying grammar system.