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Can you move through squares occupied by an opponent if he allows you?

The rules only says:

Moving Through a Square

You can move through an unoccupied square without difficulty in most circumstances. ...

Opponent: You can't move through a square occupied by an opponent unless the opponent is helpless. You can move through a square occupied by a helpless opponent without penalty. Some creatures, particularly very large ones, may present an obstacle even when helpless. In such cases, each square you move through counts as 2 squares. ...

But if he voluntarily allows you, why couldn't you be allowed?

The trigger for this question is the following situation:

A player is going from A to B where between A and B there is a large invisible creature with reach 5. The approaching wouldn't let the creature do an AoO, but if he allows the player to pass by, than he would be able to do it, or not?

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This is better handled by the rules for Invisibility, rather than the basic tactical movement rules

An important point to remember: just because a Large creature tactically occupies a 10 ft. square doesn't mean it literally fills up that square (unless it's a Gelatinous Cube or some other exceptional creature...) - just as your average Elf is not 5 ft. wide...
The tactical grid is an abstraction, its underlying assumption is that a 5 ft. square is the area a Medium sized creature needs to effectively swing its weapon, not the minimum area it can stand on.
The combat systems assumes as a default that any non-helpless opponent will actively try to block your passage (not necessarily by physically blocking your way - waving a weapon at you is equally effective...).
This is not necessarily the case for an invisible creature.

If there's a clear tactical advantage for the invisible opponent to allow you to pass it (maybe so you provoke an AoO, or so it may keep its location or presence hidden), it makes sense that the opponent may allow you to pass it - just as a friendly creature would.
The rules for Invisibility state that:
(emphasis mine)

[...] A creature can generally notice the presence of an active invisible creature within 30 feet with a DC 20 Perception check. The observer gains a hunch that “something's there” but can't see it or target it accurately with an attack.
It's practically impossible (+20 DC) to pinpoint an invisible creature's location with a Perception check. Even once a character has pinpointed the square that contains an invisible creature, the creature still benefits from total concealment (50% miss chance).

So, clearly, while you are moving near it, you are allowed a Perception check to try and notice the invisible opponent (with an insane DC 40 + opponent's Stealth check if it is standing still) - but you don't automatically detect it - merely moving past or through its area is not actively searching for the invisible opponent - that's a standard action:

A creature can grope about to find an invisible creature. A character can make a touch attack with his hands or a weapon into two adjacent 5-foot squares using a standard action. If an invisible target is in the designated area, there is a 50% miss chance on the touch attack. If successful, the groping character deals no damage but has successfully pinpointed the invisible creature's current location. [...]

Now, since there's a 50% miss chance even when you are actively searching for the creature - it makes no sense that by simply walking around you can automatically detect it: Allowing that will mean that rather than using a standard action to test 2 squares (forgoing your attacks), you could just use a move-action to test 6 squares (for normal Medium unencumbered speed) avoid the 50% miss chance, and attack the creature in the same round.

So, while the movement rules don't specifically handle this situation, it seems to me that you could handle this in one of two ways:

  1. The PC simply passes through the occupied area - it may get a "free" Perception check to allow him to notice the opponent (probably rolled secretly by the DM if the player isn't aware of the opponent).
  2. The PC still has some chance to "bump into" the invisible opponent - I'd still treat this as a Stealth vs. Perception check rather than use the flat 50% miss chance (to reflect the fact the the foe is actively trying to avoid detection, and does its best to stay out of your way), but this is really the DM's call.

Personally, I'd just use option #1.

As a side note: Even with only a 5 ft. reach, You'll still provoke an AoO when you leave the square adjacent to the invisible opponent in order to (unwittingly try to) move into its space. It does not have to allow you to pass just to hit you...

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Kinda

The closest thing to a specific rule on this is the rule for moving through an occupied friendly square:

You can move through a square occupied by a friendly character, unless you are charging. When you move through a square occupied by a friendly character, that character doesn't provide you with cover.

So, if the creature wants to let you move through its square, you could just rule that it's "friendly" at that particular moment.

This can lead to some weird cases when dealing with invisible creatures through, where you're "friendly" to let someone through, which causes them to move to a spot that's better for you, at which point you cease being friendly and take an AoO against them (or your turn comes and you can full attack). Players might want to use that tactic, but it can look suspiciously like DM cheese when NPCs do it.

It's generally simpler in the case of friendly vs hostile movement to just say "you bump into something and can't enter that square", which is how the rule works normally. They won't know what they bumped into, just that something invisible is there. If you did want to allow someone to let another creature through, I'd consider a house rule where they can't declare themselves friendly and unfriendly in the same turn. Thta is, if they do let the creature through by being "friendly", they can't immediately turn hostile and take an AoO on the same turn.

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Answer for the trigger:

I would use the rules for acrobatics for this and assume the player fails as he is unaware of the danger. The invisible creature gets an AOO as the player leaves the threatened square and if it hits the player's movement is halted there.

Personally if the attack misses then I would treat it as a bull rush with a penalty of at least -4, otherwise the player is stationary.

Generic Answer:

While there is no specific rule to cover this, it makes sense for the GM to make an exception in this case. The rule quoted assumes that the enemy wants to hinder your movement, if they are choosing not to then they would only restrict you movement as an ally (such as not being able to charge through that square).

Bear in mind that you still provoke attacks of opportunity from your enemy, who may choose not to take them. I suspect it would be quite difficult to know without some form of active communication that he wanted to let you pass. If the enemy is allowing you to because he is actually on your side he should probably be classed as an ally.

This kind of situation is why we have a DM to adjudicate, rather than using pure mechanics at all time. Your mileage may vary based on your DM.

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    \$\begingroup\$ looks like the question changed, I'll update my answer \$\endgroup\$ – Mourdos Aug 12 '14 at 12:42
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I would argue this is just an overrun.

http://paizo.com/prd/combat.html

So the invisible creature can make a reflex save to get out of the way.

I would house rule a few changes from a normal overrun:

Because the moving player is unaware of the invisible creature, and thus is running instead of crash tackling, the moving player should take a penalty on their combat maneuver check (assuming the invisible creature fails its reflex save), and if they fail by 5 or more with their check, they fall prone instead of simply stopping. However, because they are moving normally instead of attempting an overrun, it should not require a standard action to perform this.

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Both creatures have to cooperate to pass through a single square

I would treat movement as a way that can expose invisible creatures by simply running into them. I would rule that an opponent can allow you to move through his square if you both cooperate for it, but if one creature doesn't even know that the other is there, then it doesn't work - especially if the blocking creature is large.

If the invisible creature wants to avoid being detected this way, then a reasonable solution would be a ready action to move aside when/if the player approaches - that's the general rule-appropriate way for reacting to events outside of your turn. If the invisible creature wants to spend it's actions on something else than evasion, well, then it doesn't get to evade.

[That's not a detailed analysis of Rules As Written, but my personal interpretation of the rules you cited. Your mileage may vary.]

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    \$\begingroup\$ is this based on a specific written rule, or is it something you are interpreting as GM? Whichever it is, your answer would be stronger if this was made clearer \$\endgroup\$ – Wibbs Aug 12 '14 at 9:29

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