。
She watched several plays in succession.
Literal
She [topic-は] how-many even one-after-another play [object-を] watched.
Two pieces give the sentence its texture. 何本も is the pattern 何 + counter + も = 'many ~,' literally 'how-many-even.' 本 here is the counter for long thin objects, but in extended use it's also the counter for plays, films, columns, and broadcasts (a slight quirk of the counter system). たて続けに ('one after another, in succession, back to back') is a vivid adverb suggesting tight chain consumption — binge-watching or binge-attending. Together they paint a vivid picture of someone marathoning through theater performances.