I'll plug Silver Templars, they are a UM successor chapter and chapter tactic is Bond Martial, which allows melee attacks against infantry or biker to autowound on 6. Generally you will want to run small squads, so 5 assault intercessors get 11 attacks which is 1.8 auto wounds, or 3 man outrider that get 9 attacks giving 1.4 wounds. Back them up with a primaris ancient, with the Banner of Echoes relic and you can get +1 attacks for models, giving your 5 man assault intercessor 16 attacks, or the 3 man outrider 12 attacks. Can also get some really good combos with Bladeguard Vets, 3 model unit gets 10 attacks. On top of that they can re-roll 1 hit roll (which is why smaller units are preferred).

Downside is they are a primaris only chapter in the lore so terminators, and other non-primaris units won't get the benefits of their rules and stratagems that are sometimes limited to primaris only units.

TLDR you can get some good melee combos and damage output, but with the focus on primary and secondary points you aren't always incentivized to get into melee.