The purpose of this study is to identify the supports and barriers to scalability of Veteran-tailored iTBS and APT across neurologic conditions, with the longer-term goal of providing an empirical basis for the tailoring of a broader range of cognitive rehabilitation strategies to optimize each Veteran's cognitive function in daily life. After Veterans receive standard cognitive rehabilitation, cognitive impairments often persist and if they do make gains there is limited carry-over to daily function. The tenets of precision neurorehabilitation suggest that tailored interventions will optimize gains and carry-over, but precision-tailoring of cognitive rehabilitation will only be possible if researchers develop and test scalable approaches for identifying, organizing, and analyzing the multitude of Veteran-specific variables driving and influencing treatment responsiveness. This project addresses long-standing scientific barriers to understanding treatment responsiveness, particularly study sample heterogeneity and individual variability. The investigators address study sample heterogeneity by linking Veterans, across TBI and ischemic stroke, according to levels of cognitive impairment. The investigators create a cohort of Veterans with a homogeneous level of cognitive impairment, thereby enabling explication of person-centric factors influencing treatment responsiveness and carry-over to daily function. Advancing understanding of the basic study design elements will be achieved by leveraging the knowledge of intermittent Theta Burst Stimulation (iTBS) and iTBS paired with Attention Processing Training exercises (iTBS + APT). iTBS is advantageous as it robustly improves working memory with just one treatment session. These interventions, together, are advantageous as they can each be tailored to a Veteran's unique cognitive challenges and to target the neural site, unique to each Veteran's neuropathology. These two interventions also directly address cognitive deficits, while simultaneously inducing neuroplasticity in neural regions hampered or impaired by neural injury. The investigators will study Veterans with moderately impaired cognition who, after standard cognitive rehabilitation, continue to struggle with daily life requiring assistance with complex instrumental activities of daily living (IADL). Veterans will participate in a series of two within-subject treatment studies, conducted on two separate days, 2-weeks apart. Veterans will be randomly assigned to first receive a single session of Active iTBS or Placebo iTBS and then they will receive APT paired with their assigned iTBS (Active iTBS + APT vs Placebo iTBS + APT). The investigators will test if diagnosis moderates the effects of these interventions on both immediate and persisting change in cognition. For immediate effects, the investigators use a novel testing battery and for persisting gains the investigators use established and feasible neuropsychological tests as well as an established test of cognitive function during IADL. Results will be used to obtain pilot data and examine feasibility in terms of study attrition relative to Veteran fatigue, mood, and Veteran reports of suitability of key aspects of the study design. These findings will be used to develop a future merit within-subject cross-over study examining the over-arching hypothesis that tailored iTBS and APT applied to a transdiagnostic sample and subsequently matched to a Veteran, according to a biotype algorithm, will result in better functional performance of Veteran-valued IADL.