So may routes and so much rolling stock has moved between TPE and other TOCs since ATN it is meaningless making sweeping generalisations about capacity without doing some thorough research.
I have done some thorough research, albeit some of my figures for the North West services down the years are a bit sketchy. I just didn't feel it necessary to present the nitty gritty detail at the time:
2000 - Northern Spirit Transpennine Express 158
51 carriages = 17 x 3-car 158
42 carriages = 21 x 2-car 158
20 carriages = 10 x 2-car WYPTE 158
TOTAL = 113 carriages
2005 - First Transpennine Express pre-185
69 carriages = 23 x 3-car 158 (17 x original and 6 x hybrid formations)
46 carriages = 23 x 2-car 158
27 carriages = 11 x 2-car/3-car 175 hired by TPE for North West services now incorporated into the franchise (I'm not sure of how many 2 and 3-car units TPE utilised, but know that they hired 11 units on a daily basis)
TOTAL = 142 carriages including North West services
TOTAL = 115 carriages without North West services
2006 - First Transpennine Express 185/170
153 carriages = 51 x 3-car 185
18 carriages = 9 x 2-car 170
TOTAL = 171 carriages including North West services
9 x 3-car 185 units subsequently utilised on Manchester - Scotland services (rough figure, admittedly)
TOTAL = 144 carriages excluding Anglo-Scottish services
2015 - First Transpennine Express 185/170/350
153 carriages = 51 x 3-car 185
8 carriages = 4 x 2-car 170
12 carriages = 6 x 2-car 158
40 carriages = 10 x 4-car 350
TOTAL = 213 carriages
TOTAL = 173 carriages excluding Anglo-Scottish services
2020 - First Transpennine Express New Fleet/185
65 carriages = 13 x 5-car EDMU for North TPE services
95 carriages = 19 x 5-car EDMU for North TPE Newcastle/Edinburgh services
60 carriages = 12 x 5-car EMU for WCML Anglo-Scottish services
84 carriages = 28 x 3-car 185 (Numbers not confirmed)
TOTAL = 304 carriages
TOTAL = 244 carriages excluding WCML Anglo-Scottish services
Also note that at this point, the North West TPE services will have been removed from the franchise