I wrote to the New Haven Railroad Historical And Techinical Association and asked how the New Haven classed their steam.
Here's the answer I got from them:
Wheel Ar: Class No.
4-4-0 A-1
4-4-0 A-1
4-4-0 A-1
4-4-0 A-1
4-4-0 A-1a
4-4-0 A-3
4-4-0 A-3a
4-4-0 A-3a
4-4-0 B-1
4-4-0 B-2,3,4
4-4-0 C-1
4-4-0 C-2,4,6,7,9
4-4-0 C-3d
4-4-0 C-3e
4-4-0 C-5
4-4-0 C-10,11,12,13,14
4-4-0 C-15
4-4-0 C-16,17,18
4-4-0 C-19,20,21
4-4-0 C-22
4-4-0 'D-1 to 6
4-4-0 'D-7 to 13
4-4-0 'D-14
4-4-0 'D-15,16,17
4-4-0 E-1,2,3
4-4-0 E-4,5,6,7
4-4-0 E-8
4-4-0 E-9,10
4-4-0 E-11,12
4-4-0 E-13
2-8-0 F-3
2-8-0 F-5
4-6-0 G-1,2
4-6-0 G-3
4-6-0 G-4a
4-6-0 G-4b
4-4-2 H-1
4-6-0 H-2
4-6-0 H-3
4-6-0 H-4
4-6-2 I-1
4-6-2 I-2
4-6-2 I-3
4-6-2 I-4c
4-6-2 I-4d
4-6-2 I-4e
4-6-2 I-4f
4-6-4 I-5
2-8-2 J-1
2-8-2 J-2
2-6-0 K-1a
2-6-0 K-1b
2-6-0 K-1c
2-6-0 K-1d
2-6-0 K-2
2-6-0 K-3
2-6-0 K-4
2-6-0 K-5
2-6-0 K-6
2-10-2 L-1
2-10-2 L-1a
2-10-2 L-1b
2-10-2 L-1c
2-6-0 M-1
2-6-0 M-2 to M-8
2-6-0 N-1 to N-3a, b
2-8-0 P-1
2-8-0 P-2
2-8-0 P-3
2-8-0 P-4
2-8-0 P-4a
2-8-0 P-5
4-8-2 R-1
4-8-2 R-1a
4-8-2 R-1b
4-8-2 R-2
4-8-2 R-2a
4-8-2 R-3
4-8-2 R-3a
0-4-6T S-1
0-4-4T S-2
0-4-4T S-3
0-4-4T S-4
0-4-4T S-5
0-4-4T S-6
0-4-4T S-8
0-6-0 T-1
0-6-0 T-2a
0-6-0 T-2b
0-6-0 T-3
0-6-0T T-4
0-6-0 U-1a
0-6-0 U-1b
0-6-0 U-1c
0-6-0 U-2
0-6-0 U-3
0-6-0 U-4
0-6-0 U-5
0-6-0 V-1
0-6-0 V-2
0-6-0 V-3
0-6-0 V-4
0-6-0 V-5
0-4-0 X-1
0-4-0 X-2
0-4-0 X-4
0-4-0 X-5
0-4-0 X-6
0-4-0 X-7
0-4-0 X-8
0-4-0 X-9
0-4-0 Y-1
0-4-0 Y-2
0-4-0 Y-3
0-4-0 Y-6
0-4-0 Y-7
0-8-0 Y-2
0-8-0 Y-3
0-8-0 Y-4a
2-4-6T Z-1
The numbers and small letters are mods from both the manufactuer and when the loco was shopped, and mods were done .
I'm guess, this is the same system that a lot of other railroads used.
Just a guess though.