Some new ideas in the theory of teams in grammar systems are introduced and studied. Traditionally, a team is formed from a finite number of sets of productions and in every derivation step, one production 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 a maximal amount of times.
Here, the possibility of different teams having different modes of derivation is defined, as is a weaker restriction on the application of a team. The generative power of such mechanisms is investigated.