one-star, two-star, three-star, etc. (all AmE)

command sth, lead sth
Both generals had commanded units in that area.

General is used with these nouns:
acceptance, acclaim, administration, adoption, advice, agreement, aim, amnesty, anaesthetic, apathy, appearance, application, approach, approval, argument, aspect, assembly, assent, assertion, assessment, assumption, atmosphere, attitude, audience, availability, awareness, background, belief, category, chaos, characteristic, check-up, chorus, circulation, classification, collapse, comment, commitment, concept, conception, concern, confusion, consensus, consent, context, conversation, correlation, counsel, criticism, currency, decline, decrease, description, direction, directive, disarmament, disarray, discontent, discussion, disillusionment, dislike, dissatisfaction, distaste, distinction, distress, distribution, distrust, drift, duty, editor, education, election, electorate, enquiry, enthusiasm, euphoria, expectation, expenditure, explanation, failure, fatigue, fear, feeling, finding, fitness, framework, gist, gloom, guidance, guide, guideline, heading, health, hospital, hostility, idea, ignorance, implication, importance, impression, improvement, index, indication, information, insecurity, instruction, insurance, intention, interest, introduction, knowledge, labourer, lack, layout, level, library, maintenance, management, manager, maxim, medicine, meeting, membership, merchandise, mistrust, mood, murmur, nature, neglect, notion, nursing, observation, opinion, outline, outlook, overview, panic, pardon, partner, perception, philosophy, physician, picture, population, practice, presumption, principle, prohibition, property, proposition, prosperity, public, purpose, reaction, reader, recognition, recommendation, reduction, reference, rejoicing, relaxation, relevance, reluctance, remark, report, requirement, revenue, rise, rule, run, scepticism, secretary, sense, sentiment, shape, shortage, significance, similarity, situation, staff, store, strategy, strike, summary, supervision, support, surgeon, surgery, survey, sympathy, taxation, tendency, tenor, term, textbook, theme, theory, thesis, thrust, tone, topic, trend, truth, understanding, unease, unhappiness, usage, use, usefulness, verdict, vicinity, view, warranty, welfare, well-being, will, willingness