So, I've been thinking a lot about how Tecmo could possibly come up with another good MR that people would love, and I've been reading most of these threads. A common element I see is that people want what they're comfortable with: All of the old monsters back. So, I've come up with about 600 monsters that cover all of the old ones, as well as some new combinations that would be within reason. However, that isn't what I was looking for, because as it's been said here, it isn't about the quantity of the monsters, but what you do with them.

So, I think it'd be convenient to expand on the existing ideas. In MR1 we had jobs, that are drills that give money. In MR2 they don't give money, and people don't like that. Perhaps you could have both, therefore having three categories under Training. The jobs would give money, but if you do the drills instead of jobs, then the stat increase is 1-3 higher.
Other existing features include the Wanted list at the errantries. This could be expanded on for a really cool feature, and would even give another way for trainers to focus their monsters. Breeders train monsters for battle or for expeditions (or breeding, but ya know). If they expanded on the Bounties, then it could be a whole new idea. If a monster runs away from you, then there's a chance it won't come back. This chance is higher if you treated it badly. If it doesn't come back, then it will become a bounty at an errantry. If you defeat a monster in errantry and do 10% or less of its health in excess damage then you do not get paid the bounty. If you do 11% to 20% then you physically catch the monster, and you're paid the bounty. That monster is then offered to be put in your freezer, or you can sell it at the market. 21% to 60% results in injuring the monster, and you get paid the bounty, and the monster will be sold to another trainer, possibly appearing in unofficial tourneys of whatever grade it was in. 61% and up are death hits, which give you 1.5x the bounty, but kill the monster.
With how much Tecmo does with percentages and numbers, this wouldn't be much, but it would greatly expand on the bounties. Also, tourney monsters' stats will increase if they win a tourney by average battle increases, and if you see another monster win an official battle then they'll appear in the next grade up, being replaced by a new monster.

Expeditions could be expanded on by firstly, having you go with. You could accompany the monster into the buildings and have some sort of minigame (which I'm not sure on. I'd love some ideas on that). Items would all be fond in the same percentile, and reaching everything would be the same, except for not having an aerial view, but more of a FPS view, watching your monster as it walks where you direct, and destroys obstacles likewise.

Errantries could also have multiple outcomes, not always fighting a polar bear at the end, but perhaps fighting a Narwhal that breaks through the ice. Different animals will likely result in different stat gains, attacks, and the wild enemy you face (The polar bears give +speed and health, while the Narwhal gives +speed and power).

We know of all sorts of locations, both within Fimba as well as IMa. Being able to live in ten different backdrops in two different regions wouldn't use much (How much time does it take to make four backdrops per location (due to seasons). More house upgrades, stable upgrades, fence upgrades to decrease the chance of a runaway. Having a feature to save a monster for 1Pv2P gameplay would be awesome, as you could save all of your monsters into it, without a freezer limit, and then combine it as needed. When a monster dies it would give you the option of saving it before it passes on. This would bring more attention to the versus mode, which can grow stale after fifteen matches.
The test you take in the beginning has meaning. It will change who your ranching assistant is. If you're playing in Fimba you could get Holly, or a dozen familiar faces from MRBC:epi.II, and in IMa you could get Colt or more from that game.

Any other ideas that people would like to see that aren't new, but expand?

I have an idea for the building minigame. My friend and I thought that if you could have a top down view of your monster and you would have doors to choose from and sometimes unseen hazards like a door got blocked and you had to use a tech to open it but if your monster over exerts itself it could become sick or injured. There would also be these random things called "greed chambers" that had 4 boxes. 1 has tresure and 3 have bombs or somthing that KO your monster and cancels the expedition plus it would cause a hit to your monsters overall lifespan. In the building there would be a weak miniboss that when you beat it gave you a small tresure. There would also be a standard boss that would give an item better than the minibosses item. when you beat both monsters you beat the building.

The test you take at the beginning actually changes the advice your assistant gives you I believe.

Yeah, I run through a lot of ideas every so often...

Zilk, I like the idea. It'd be cool to see that smoothed out a bit. Also, I don't know how I forgot, but integrating a theme like we have in MRBC:Epi.II would be amazing. Cards could be prizes in run-o'-the-mill tournies. Cards would be gotten when you learn an attack with a monster, or when you get it from a disc or in combining. Every monster would have a card, and since in MR2 they made every card anyway, it isn't to outlandish of an idea. It'd be a lot more cards for the attacks, but the attacks would only be for each main type, not each monster. Also, for a brief list of some of the trainer's assistants that would theoretically be available:

Cue, Colt (IMa), Holly (Fimba), Stolatos, Isabella (She could even let out the occasional "••••" or "hell" for a comedic factor. i.e. 'Look at the •••• thing! Give it some rest!'), Penny, Cocochino, Claire, Yilis, Frederika, Miller (He'd be perfect, too), Ellie, etc.