Out of curiosity, i went through variants of various TRO3025 'Mechs and counted who made most variants.
I only counted up to 3030 or so, since Star League era.
I excluded advanced tech variants such as the TDR-5Sd (Davion upgrade during the Star League) or the TDR-5L and -5LS (Capellan SW-era downgrades from -5Sb), Royals, and the oddball LCT-3L (TSM testbed).
Nation exclusive or near-exclusive 'Mechs were ignored (such as the Dragon), and Inner Sphere-wide variants (eg Atlas RS) aren't counted either.
Liao:
8 variants
Kurita:
12 variants (one imported), 13 if the Whitworth 1S is counted since only Dracs retained it during the Succession Wars
Davion:
16 variants
Steiner:
8 variants
Marik:
8 variants
Mercs:
3 variants
The Federated Suns tinkered far more than any other faction, having twice as many custom variants as most. Many variants are pretty late though, like the Blackjack and Rifleman variants (4 total), i presume these derive from Hanse Davion's initiative to preserve research and expand upon it.
Interestingly the Draconis Combine tinkered almost as much with their 'Mechs as the FedSuns did. Their variants have tendency to be more aggressive. The Trebuchet and Catapult variants shy away from indirect fire, and many others either increase firepower directly or increase cooling and thus increase firepower. Suits their Samurai tendencies i suppose.
Others are pretty modest.
The FWL variants tend to make use of large lasers or otherwise replace PPCs.
Most of the Capellan variants seem to be experimental, trying to make better use of a 'Mech chassis (Charger, Cicada).
The Lyrans did a bit more than my list indicates, since the Commando and Zeus both have several variants but then again the 'Mechs are essentially exclusive to them so they don't really count. Otherwise, they don't really have any particular theme.
Of the 'Mechs i looked at, only 3 had merc-specific variants, the Thunderbolt SE from the Eridani Light Horse, and the Wasp and Archer W variants from the Wolf's Dragoons.
Presumably mercs don't really have chances to create their own standardized variants. The ELH's T-bolt variant is unusual because of this. The Wolf's Dragoons having variants isn't odd considering their capabilities, but i have to wonder if the variants originate from the Clans in some way?
Though i don't list it, the ComStar made one variant, the Battlemaster 2C, dating from 2925. What happened during that year?
One interesting thing is that contrary to popular perception, there are few more variants whose designation doesn't match the fielding nation rather than just the LCT-1M. I've noted those in the list below. But i suppose it is not a surprise people don't recall these, they're either kind of bad or obscure or of limited use otherwise. Like the Trebuchet is best remembered as LRM 'Mech, who recalls it has a SRM variant?
Variant list, Great House mentioned where designation doesn't match expected nation, also other notes:
Wasp 1A
-1L
-1K
-1D
-1W
Locust 1v
-1S
-1M (Davion)
-1E (originally Capellan, spread everywhere)
Phoenix Hawk 1
-1K
-1D
Shadow Hawk 2H
-2D
-2K
Wolverine 6R
-6K
-6M
-6D
Griffin 1N
-1S
Rifleman 3N
-4D (Davion)
-3C (Davion)
Crusader 3R
-3L
-3D
-3K
Thunderbolt 5S
-5D
-5SS (Steiner)
-5SE (Eridani Light Horse)
Archer 2R
-2K
-2S
-2W
Warhammer 6R
-6L
-6D
-6K
Marauder 3R
-3D
-3M
-3L
Battlemaster 1G
-1D
-1S
Banshee 3E
-3S
-3M (Marik)
-3Q (Marik)
Awesome 8Q
-8R (Marik)
JagerMech S
-A (Davion, possibly Star League/FedSuns factory variant)
Catapult C1
-K2 (Kurita)
Trebuchet 5N
-5J (Marik)
-5S (Marik, spread elsewhere)
-7K (Kurita)
Hermes II 2S
-4K (Kurita, export model from FWL)
Cicada 2A
-2B (Liao)
-3C (Liao)
Assassin 23
-101 (Davion)
Spider 5V
-5D (Davion)
-5K (Kurita)
Charger 1A1
-1L
-1A5 (Liao)
-SB (Steiner)
-1A9 (Kurita)
UrbanMech R60
-R60L
Blackjack 1
-1DB (Davion)
-1DC (Davion)
Ostroc 2C
-2M
Ostol 4D
-4F (Davion)
Victor 9B
-9S