I am three words, Two of them appear the same, Two are pronounced the same. One is the third person use of "capable" or "permit". One means to sleep, but only for a bit. The last word means a group of deer, Perhaps now you can tell me, what words are here?

“Can, Nap, Can”

While 'Can' is a synonym for 'capable' and 'Can' is pronounced the same, 'Nap' does not mean to sleep for a bit. Additionally, 'Can' is not the correct third word, which should be 'Does'.

“Able, Snooze, Able”

'Able' is not a word that fits the riddle's requirements since it doesn't represent the third person use of 'capable' in the same structure as 'Does'. 'Snooze' is synonymous with 'sleep' but does not match the riddle's phrasing, and 'Able' repeats incorrectly.

“Might, Rest, Might”

'Might' does not fit the definition of the third person use of 'capable' as it is not the correct form; 'Rest' does imply a brief sleep but doesn't match the wordplay, and 'Might' is incorrectly repeated.