The new Raleigh variant, the Stortebeker, is literally built for this. You can do it one of two ways:
1. Slap two Main melee weapons in the Flex slots and a powerful loading weapon in the Heavy slot. I recommend the Bolt Thrower which comes with the Raleigh 2 license because it doesn't have the Ordnance tag. In terms of Main Melees, two Charged Blades are never a bad idea but if you have spare LLs available you can grab Nelson 1 for the War Pike. For those with many LLs to spare, instead grab Mourning Cloak 3 and run two Variable Swords. Having the first level of the Duelist talent is functionally a requirement for this build.
2. Slap four Hand Cannons in the Flex slots and a powerful melee weapon in the Heavy slot. The Kinetic Hammer from Raleigh 3 is an obvious choice, but if you're feeling truly decadent you can splash all the way to Balor 3 for the Nanobot Whip. If you've only got two LLs to spare, the GMS standard Heavy Melee Weapon is a perfectly respectable choice. If you're at LL3, applying the Auto-Stabilizing Mounts Core Bonus to your Heavy melee weapon is a very good choice.
The Stortebeker has a trait called Dynamic Reload, which says that if you crit with a non-Auxillary melee weapon, you reload all ranged Loading weapons that weren't fired this turn. (Technically it also works the other way round, but because only one Loading melee weapon actually exists in the core book, this is way less relevant)
The Stortebeker also has Truesilver. Once per fight, it lets you turn a regular hit with a non-loading weapon into a crit. This doesn't change the damage it deals, but it does cause all of an attack's on-crit effects to trigger, including Dynamic Reload.
The basic idea here is that you run on a two-turn cycle. On the first turn, you slam in with your loading ranged weapons, dealing tons of damage. The next turn, you slam in with your melee weapons, fishing for crits to reload your ranged weapons with. This is why Duelist 1, the Variable Sword or an accurized Heavy melee are so powerful - having at least point of Accuracy significantly increases your chance of landing a crit. If you really need your ranged weapons back and you didn't get a crit, you can use Truesilver to convert a regular hit into a crit.
If all else fails, the Stortebeker has two additional options: Hopkins Doctrine, which lets you reload all Loading weapons not fired this turn as a quick action, and your Ult, Truesilver Arsenal, which simply lets you use Truesilver three more times this fight.
