In this chapter, we present ergodic theorems with explicit upper bounds for convergence rates for multi-alternating regenerative processes modulated by uniformly recurrent semi-Markov processes. We consider uniformly recurrent semi-Markov processes and get uniform (in the class of all initial distributions) upper bounds for tail probabilities and power and exponential moments for hitting times for such semi-Markov processes. We give two series of ergodic theorems with explicit power and exponential upper bounds for convergence rates for multi-alternating regenerative processes modulated by uniformly recurrent semi-Markov processes with atoms and for multi-alternating regenerative processes modulated by uniformly recurrent semi-Markov processes admitting artificial regeneration. Also, applications of ergodic theorems for multi-alternating regenerative processes with semi-Markov modulation for getting variants of semi-Markov renewal theorem with explicit power and exponential upper bounds for convergence rates are discussed.