A Holmes Alternative to High Level Combat

A while ago I made a post here regarding Geoffery's post at Dragonsfoot regarding the potential of a "Holmes-only" campaign.

While browsing some old posts at Dragonsfoot I came across this one: Holmes: Looking better with each reading

The thing that struck me is that, as pointed out by Thorkhammer, under the Class descriptions, pages 6-7, Holmes clearly states that Fighting Men,

"after they reach the fourth level of experience, they also increase their ability to get hits on an opponent..."

Fighting Men includes Human, Dwarf, Hobbit and Elf. There is no such reference for Cleric, Magic-user and Thief. I know that Holmes says to go the AD&D for higher levels and that the intent is that everyone improves at combat. I, however, like the idea that Fighting Men (and their derivatives) are the only ones to improve at combat. Why should a magic-user get better at attacking with his dagger?

If someone wanted to run just the Holmes book and expand it to higher levels (there are a number of excellent examples on the net) there could be another way to handle improvement at combat.

The thought that came to me is that you could reflect the improvement of Fighting Men to "increase their ability to get hits" by giving them extra attacks per round instead of expanding the attack tables. Allow an extra attack per round. Fighting-Men get 1 attack / round for levels 1-3, 2 attacks / round for levels 4-6, 3 attacks / round for levels 7-9, etc...