I will be talking about Metal Gear Rising project and prospect of a sequel.

How did the project begin?
First off MGR was a spin off experiment for the younger developers to become better at Metal Gear. Kojima's objective was to make the younger developers reach a level of skills so that he could pass the development for major SOLID games to them.Since that responsibility was to big, they did a spin off instead. Kojima wanted it Gray Fox to be main character but his team wanted Raiden.
Platinum Games on board
The team had issues with designing the game based on the concept of cutting things. Blade mode...So the project was on hold, until at a party Kojima casually asked Atushi Inaba if PG wanted to develop MGR. PG accepted.
Why did Metal Gear Rising turn out as it did - above average?
I think from a gameplay perspective, time constrait had a significant role. I believe Platinum Games had roughly 2 years to develop the gameplay.
Here is a quote from a PG developer:
Any studio has its specialities, and things it excels at, and we only had a limited amount of time to create Revengeance for our specific deadline. We had to sacrifice a few things, but if we were to work with Kojima studios in the future, we’d like a little bit more time to show a little bit more of Platinum Games’ unique points that we excel at.
And a quote from Kojima:That, and we gave a deadline. It was pretty rough schedule, to be honest, but we got it done with hardly any delays. For a title of this size, even if we had an archetype to work with, it was developed astonishingly quickly.
So tight schedule, quickly developed, deadline and a developer expressing need of more time for a possible sequel is a clear indication that development took a blow that demanded more compromiss. Because even with 3 years development, compromiss must be made.
Perhaps this constrait affected even the story?
The Passion of Kenichirou Yoshimura

He was one of two who worked on characters for MGR. Here is pharagraph written by him on PG blog:
Three days before I was about to leave Platinum to go freelance, without much left to do, I strolled over to the nearby Rising team to see if they needed any help. “I could design something small, if you wanted,” I said.
Then I saw their designs – the art style could not have been further from the Metal Gear universe. Immediately, I slammed my fist on the director’s table. “You cannot put this in a Metal Gear game!” I told him. Before I knew it, my last three days at Platinum turned into over half a year.
I’ve played through the entire Metal Gear series and I share the same impressions as so many other fans – Shinkawa-san does unbelievable character and mech design. I collect all the art books like everyone else, (not to mention that I love Z.O.E., too.) so if you had told me I was going to be working on a Metal Gear game someday, I never would have believed you. Joining the team, I was as excited as I was terrified.
Metal Gear Rising sequel?

This is what Kenji Saito said about Kojima production:
One big difference I think all our staff believe is that Kojima Productions is almost too detailed when it comes to its settings. [Everything is] so precise, and that level of detail is something that Platinum Games has never experienced. It’s not necessarily a bad thing, and we believe that keen eye has made our staff a lot better. That’s something we can take back for our games in the future.
Hideo Kojima thoughts on PG:Honestly, I’ve been making games for over 25 years and the state that this game was in when it went to Platinum... was really a mess! The fact that they were able to pull it off is very impressive.
"As far as [Metal Gear] Rising 2 is concerned, I really do have that in my mind, and I want to make it," Kojima explained. "And if we do make it, it would definitely be with Platinum. I don’t think anyone else could do it.
Now imagine Metal Gear Rising 2 with standard development time with Fox engine and Kojima team collaborating with Platinum Games. Kojima taking the story, Platinum the gameplay.
Sounds pretty great if you ask me.
And it could happen...Konami is Rising.