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The paper studies the optimization of average-reward continuous-time finite state and action Markov decision processes with multiple criteria and constraints. Under the standard unichain assumption, we prove the existence of optimal K-switching strategies for feasible problems with K constraints. For switching randomized strategies, the decisions depend on the current state and the time spent in the current state after the last jump. For stationary strategies, these functions do not depend on sojourn times, i.e., they are constant in time. For K-switching strategies, these functions are piecewise constant and the total number of jumps is limited by K. If there is no absorbing states, there exist also optimal K-randomized policies. We consider the linear programming approach and provide algorithms for calculations of optimal policies.