Counting a repertoire means recording a male at length and sorting phrases on spectrograms into distinct types. Brown thrashers make this laborious. A singing male delivers a long, unbroken run of varied phrases, most of them repeated twice before moving on, so a single bout can contain hundreds of different units.
Published estimates for the species run from several hundred to over a thousand song types, with the higher figures widely quoted. The uncertainty is methodological: how finely two phrases must differ before they count as separate types is a judgement, and different analysts draw the line differently. The honest statement is that the repertoire is very large and difficult to enumerate exactly.
The doubling is a useful field mark. Mockingbirds typically repeat a phrase three or more times, thrashers about twice, and catbirds usually once with no repetition. The three mimids can be told apart on that rhythm alone, without seeing the bird, which is often the only option in the dense cover a thrasher prefers.