I enjoy that style of play. We called it "expedition" play rather than troupe play. It was a holdover from Keep on the Borderlands, where each sortie to the Caves of Chaos left the keep with 20 or so hirelings, and came back with 4-5 survivors. Rich survivors. This was with OD&D in the 1980s.
You could run a henchmen-heavy game in 5e pretty easily, with each acting on their own initiative. Or you could do it 13th Age style, and aggregate your henchmen into one "creature". One attack per round, good damage (something like d10, +1 per henchman), with a HP threshold instead of a pool of HP: for every 8 HP of damage from a single attack, lose a henchman. Multiples of 8 (or whatever) damage remove multiple henchmen; "extra" damage is discarded and not tracked.
That'd simulate something like the group of warriors that accompanied Perseus in Clash of the Titans, or your typical squad of sellswords.