The autoresonant approach for the generation of dark solitons by external fields is developed in the context of the effects of mode-locking instabilities which occur in multi-phase driving. The one-phase step-by-step and two-phase drivings are studied for slowly varying frequencies of the drives. Possible scenarios for the stable generation of high-depth dark solitons are found. Adiabatic control of soliton parameters is demonstrated when the driving amplitudes exceed a threshold. The driving amplitude diagrams for preferable scenarios of the generation of high-amplitude dark solitons are presented.