BAbSANT (Bilingual Abstract Semantic Associative Network Training) is a novel, theoretically motivated approach to anomia therapy for bilingual persons with aphasia (BPWA). We report on a Russian-dominant, Russian–English BPWA, who was trained on abstract English and Russian words. We hypothesized both within- and cross-language generalization when the non-dominant language was trained, and only within-language generalization when the dominant language was trained. We also hypothesized that cross-language generalization is modulated by nonverbal cognitive control. Results revealed that when English abstract words were trained, within-language generalization to concrete words and cross-language generalization to Russian abstract words was observed, confirming our first hypothesis. However, our second hypothesis was not confirmed. When Russian was trained, direct effects of treatment and within- or cross-language generalization effects were not observed. Our third hypothesis was confirmed. Results from cognitive control tasks from this individual suggest a role of nonverbal cognitive control on cross-language treatment outcomes.