I'm writing a story, with several POV characters.

There's an upcoming scene, that would be experienced simultaneously by at least 3 and at most 4 POV characters.

I plan to cover the scene, and all the characters thoughts, reactions, emotions, etc.

This is very important, because the scene would include among others; a battle of wits, characters trying to feel eachother out, observations and responses from third parties, etc.

This chapter, is very pivotal to the story.

I'm wondering how to go about it?

Well with so little information I'm not sure what to say. I'll ask random questions and give random opinions for now.

First, I take it it's a long scene ? Because if it's short, there's the risk/option (depending on your taste) of having a lot of one or two-paragraph-long POVs. It can either make for a fast paced scene with quick jumps between the character's POVs, or it can end up as  annoying and repetitive comings and goings between POVs. I think the longer the scene, the better - it'll allow you to develop each POV in depth, with the thoughts, guesses and strategies of the characters.

As for the order/choice of POV depending on the situation : I've read somewhere (can't remember where) that when there was a battle (physical or mental, doesn't matter) to tell, you should always use the POV that allows the tension to be conveyed in the most impactful way.
For instance, if two guys clash in a fist fight, show the POV of the one being pressured. His frenzied thoughts, the chaos in his mind as he tries to keep up with his opponent, etc.
Or else, if you have cunning people facing off, show the POV of a spectator : actions and decisions that seem confusing at first in the character's mind only to make sense after a while, or having the character misinterpret things and then blowing the reader's mind as the character recalls an important detail and realize the plan, etc.
Since you'll be describing a battle of wits and guile, you should really play with the character's interpretations of events, the pressure and the tension that they feel, showing a character's POV as he thinks he has the advantage only to show another POV after that proves he's being tricked... Things of the sort.

I don't really have anything else in mind right now. If you want to give a few precisions I'll try to think of other things !

The scene is a date.

The two characters on the date are special; one is the MC , and the other is the MC's arch nemesis' younger sister. Both characters know that the other is not what they appear to be, and are wary of the other. They are also interested in the other party on a romantic level as well. They have their date, while feeling each other out, carrying out mind games, trying to guess the other's identity, etc.

The other two characters, are chaperones.

On the MC's side, his maid/robot/sapient AI is observing the date, and observing their surroundings. Trying to figure out the other party's objectives, taking note of threats to the master, reacting etc.

On the younger sister; Princess Anastasia's side, her brother's right hand Duke Alvin is watching the date as well. He suspects MC to be the arch nemesis of KIng Arthur, and is trying to feel out the MC, and such.

A lot of mind games, mental warfare will be taking place during the course of the date.

The date scene, should be a few 1000 words I expect, but it wouldn't be the only scene in the chapter.

My chapter length, are planned to be from a few 1000 words to tens of thousands.

If you are writing in the First Person POV, I don't recommend switching perspectives anytime within the story unless you can differentiate every perspective's inner voice and make it obvious as to who's POV we are in (<that's like having an entirely different writing style for every character perspective you take).

If you insist on entering every perspective in a single scene, then I'd suggest the Third Omniscient POV similar to how 'The Hitchhiker's Guide to the Galaxy' was written (much like a 'story-telling' style).

Here's a reference link further explaining POV if you need it:
http://www.scribophile.com/academy/using-third-person-omniscient-pov

'Chiisutofupuru' pid='822389' dateline='1489690497' Wrote: If you are writing in the First Person POV, I don't recommend switching perspectives anytime within the story unless you can differentiate every perspective's inner voice and make it obvious as to who's POV we are in (<that's like having an entirely different writing style for every character perspective you take).

If you insist on entering every perspective in a single scene, then I'd suggest the Third Omniscient POV similar to how 'The Hitchhiker's Guide to the Galaxy' was written (much like a 'story-telling' style).

Here's a reference link further explaining POV if you need it:
http://www.scribophile.com/academy/using-third-person-omniscient-pov

You don't think it'll be bad if I suddenly incorporate 3rd person into a multiple first person story?

In my story I have a single POV so it may not be relevant. However, I find that as long as I put a break between my POV and my third person narrative, it usually works out.

By break, I mean just make it clear that you are now writing from a different perspective. I do this by throwing a *** between paragraphs. I also try to move the story forward with each POV change. As a reader I find it boring to read the same series of events over and over again, unless the new POV has something fresh or unique I couldn't get from the other POV.

Here is an Example:

‘This is it,’ I think. ‘My first life or death battle.’

I heft my spear in my hand, reaching to unsling my shield from my back.

***

Ra’hel sat in her coils, watching the human with an enchanted gaze. The party stands on the side of paved road, watching a group of monsters go by. Startled by the trio of Ogres pulling a cart of what looks like ore, the human ‘Snowflake’ tensed for a fight. His spear held at the ready, he unslung his shield, just to be soothed by the Angel.

Standard professional writing style is to not change between first and third person during your story. There are exceptions, but not for something as straightforward as this.

First person POV with POV switches is... dangerous. There are many people who don't care, and a few people who loathe it, and then quite a few more who will read it but not mind it.

I think the advice you've received so far is valid - especially about considering how long you're spending on each POV, so you can make sure that it's distinct. I would spend at least two thousand words on each one, and maybe visit a few twice for an extra thousand each time. But then I tend to write long chapters.

Okay, so I'm linking an article I found very helpful when I was doubtful about my 1st to 3rd person perspective changes. The basic premise is that you can really do whatever you want as long as the reader isn't confused.
http://www.advancedfictionwriting.com/blog/2012/05/16/perfecting-that-pesky-point-of-view/

It is a good read. I recommend looking over it.

'SeaGangster' pid='822511' dateline='1489837361' Wrote: Okay, so I'm linking an article I found very helpful when I was doubtful about my 1st to 3rd person perspective changes. The basic premise is that you can really do whatever you want as long as the reader isn't confused.
http://www.advancedfictionwriting.com/blog/2012/05/16/perfecting-that-pesky-point-of-view/

It is a good read. I recommend looking over it.

Thanks. I checked it out, and it was quite good. 

I'll use third person POVS for chapter that has multiple POV characters.