In ten clues the wordplay leads to the answer plus one extra letter. These letters in clue order give a name (two words) to which are questionably attributed the unclued lights (in Brewer), which make three phrases: one of six words, one of three, one of four (thematically five?).
 

Across

4    See me in especial trouble, not all at once (9)
10    Confused playwright about to get between the sheets (10)
11    One stranded, pot appearing empty (6)
12    ‘With band in hair’ — poem in neat Scottish (7)
14    From Lincoln, obtain produce (5)
15    Pope is to agitate, forgetting Latin (5)
16    Off course? Just like...