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We have performed a theoretical study and made an experimental realization of a multi-frequency self-injection locking of an external cavity laser, composed of a gain-chip and an external mirror, to a high-Q-chip-scaled ring microresonator. We use a numerical model based on the rate equation system that accounts for spontaneous emission to describe a semiconductor laser and optical feedback from a high-Q cavity. It allowed us to investigate dynamics of the system and to find out regimes when several locked lines are emerged simultaneously via power redistribution over the frequency domain. Due to the well-known phenomenon of mode competition, the multi-frequency regimes appear only when several conditions are met, otherwise only single-frequency locking regimes may occur. The performed experimental investigations have shown that it is possible to achieve such states deterministically if these conditions are fulfilled.