In old science fiction stories, it was common for three planets, Venus, Earth, and Mars, to be reasonably habitable for humans and to all have human or nearly human intelligent lifeforms at the same time. Possibly that would actually be the cases in our solar system if the masses and orbits of the three planets had been somewhat different.
If you suppose that our sun has a wide and optimistic habitable zone instead of a narrow and pessimistic habitable zone, then you can fit more planetary orbits into that wider habitable zone.
You can see various estimates of the inner and/or outer edges of the habitable zone of our Sun here:
If you go with a wider habitable zone and make the planets orbit closer together then you can squeeze in four or maybe five planetary orbits around a star like the Sun.
And you could make some of the planets in the habitable zone double planets with both planets habitable.
Thus you should be able the squeeze in between four and ten habitable planets around your star. And that should be rare enough that you might have characters who know a lot about planetary science saying that the system is a very rare type, one in a thousand or one in a million.
If you have a group of planets orbiting around one star, or around both members of a close binary star, you can have another single or double star with planets orbiting it or them in your solar system, making it a double, triple, or quadruple system.
But each single star, or binary star, has to orbit sufficiently far from the planets orbiting any other single or double star in the system to not perturb the orbits of those planets. Thus at a minimum the stars (or close pairs of stars) in a multiple system must orbit at a distance several times that of the outermost planets that have stable orbits.
So travelling between different planets orbiting different stars in a multiple system will be a lot harder than traveling between planets orbiting the same star, though still much easier than interstellar travel.
And if you need even more habitable planets in your solar system, then you might have it be such a rare type that it is one in a billion or one in a trillion. Or the characters might speculate or know that this particular star system was artificial, assembled by super advanced alien beings.
Sean Raymond, in his PlanetPlanet site, has a section devoted to designing star systems with many habitable planets - tens, hundreds, or thousands - that would have to be created by super advanced civilizations instead of coming into existence naturally.
Wow! He's up to a million planets now!