Unfortunately, as you've noted, you can only take on a single hunt at any given time. This drastically slows down the process of raising your Hunter Rank.
To make matters even more difficult, based on posts in threads like this one, it looks like Hunter stars are a finite reward and completing every hunt in the game will land you at level 10 exactly.
I've done practically all the bounties, and I cant find anymore to do. Im rank 9. Im 28/43. Am I suppose to do something to unlock more hunter quest? Ive done all the dungeons, done the story, even the pitoss dungeon. What else is there for me to do to reach LVL 10
It's possible that you missed a location for its hunts, I suggest having a checklist of each outpost / town and going to all of them just to confirm you did every hunt at each, I did similar things in games where I thought I did everything, but I just missed one area because the map showed me as having it available so I just assumed I went there.
Don't forget the newly unlocked rank 9 hunts at Hunter HQ. Iirc, they all add up to 15 points. Could very well be what you're missing.
I summed the Stars column in this chart and the result was 293 stars.
From this list of Hunter Rank requirements, the requirements for each level are:
5, 15, 30, 50, 40, 40, 40, 30, 43
These add up to 293, as well. Thus, in order to reach Hunter Rank 10, you will have to complete every Hunting quest in the game.
The most optimal method for leveling up your Hunting Rank is, unfortunately, to do every hunt as you encounter it. If you only do multiple-star-reward hunts, you'll end up having to backtrack and find all of the one-star-reward hunts you skipped. If you're doing the last hunt at a specific location, it might also speed things up marginally if you just go to the next tipster, since you can turn in hunts to any tipster.