The HeroQuest base game handles it by allowing one player to control more than one hero and advises against using less.
Gold is divided among the survivors, so fewer heroes means more gold per hero as well.
But it is also true that having four heroes, especially controlled by one person, can make the game take longer (the player is having to manage more things, vs. each one having their turn ready to go just waiting for their turn).
Then again, one hero by themselves is going to be mobbed by monsters, not being able to take advantage so much of techniques like blocking doors and forming a protective screen when searching for treasure to avoid wandering monsters. They will have to fight (or run) from all monsters by themselves. And if they are not the Wizard or Elf, they may have a harder time healing (but the Barbarian and Dwarf have more body).
The Dwarf by himself is a good choice if you are going solo since he starts with the ability to disarm traps.
Still, there are solo rules out there. The Solo Quests in Barbarian and Elf Quest Pack are of little help since they have extreme (I would say broken) difficulty which is a common opinion shared on these forums.
The Dave Morris novels have solo quests (
Growl of Thunder, Running the Gauntlet) which are much easier. These are probably too easy, but his technique was to have the solo hero discover a prisoner that can be freed and assists the solo hero as an npc. (Wizard solo finds a Barbarian ally... Barbarian solo finds a Wizard ally). The Ally may be a full fledged hero but may be wounded (not have full BP) or have some of their spells already used up. But here you can do whatever you like. Maybe you find a prisoner with no weapons and only 2 BP, but nearby is a chest or weapons rack which lets you load him up with some gear, a weapon and maybe even a piece of armor. The treasure all goes to you, or maybe he collects a fee for his services (which you can't get back; don't pay it and he runs off on his own).
In other words, you're adding mercenaries (which you normally can't hire until after you become a champion, but you can say they were prisoners rather than guys you went out and hired). But then you have the same issue as above, in which now the game takes longer because they have to decide how to manage multiple characters (but it gets easier with more hands on deck).
You can certainly do what you like, but the game as written is really intended to just have fewer players control more heroes. It is a game, in the end. Only the Japanese edition billed itself as a "Role Playing Game," despite the common themes.
Space Crusade also uses the "party" technique, in that game you control a squad even though your commander is the most important character.
Now then maybe you don't want to use four heroes. You could just say 2 heroes, and give them extra gear to make up for the lack of the others. Pair a magic user with a combat character. Or maybe give the two magic users some extra armor. If there's no Dwarf, add a Toolkit for the stronger character. Or perhaps just give the two heroes a couple of potions or spell scrolls (stuff that gets used up)? Again, up to you. Just keep in mind more cards = more time per turn if you're trying to keep things moving along.