Maximum foes on battle map

I'm a new DM with a mix of new and senior players. In our last session a question came up in combat.

When a PC is surrounded on all sides on a square grid battle map, how many foes can attack?

I believed that any creature with reach could attack, the senior player believed it was a max of 4 and that corners didn't count. I'd love to get the official word from Paizo in regards to this issue. Thanks!

There is no maximum limit on the number of attacks that can be directed at a single target.
Considering only enemies with a five foot reach who are on the ground, there are eight adjacent squares to the surrounded target. All eight can attack with however many attacks they are entitled to.
You could even add a ring of 16 enemies with reach weapons. The target will have a cover bonus because of the adjacent attackers, but all 16 of the reach weapon armed enemies can attack as well.

WARNING: BAD ASCII ART

R.R.R.R.R
R.A.A.A.R
R.A.X.A.R
R.A.A.A.R
R.R.R.R.R

Corners absolutely count. If you are working in 2D (as in not working with flying or burrowing enemies), then you can have 8 creatures adjacent to another one and able to attack. Throw reach on top of that and you can have a lot more attacking, although if they are attacking through the square of another creature then they suffer the penalties of cover (+4 AC).

As an aside, I (and probably everybody else who will respond to your question) am not a representative of Paizo and my word holds no official weight. However the vast majority of rules questions are answered by the community, with veteran players taking the time to help others understand the rules better. Usually only very difficult rules questions get an official response, and this is a very easy question.

Hope this helps!

NNRNN
NXXXN
RXPXR
NXXXN
NNRNN
N = No Attack, might be wrong as Reach is a bit iffy
R = Reach only
X = Attacker
P = PC
Corners do count.
Also see Flanking.

THANK YOU SO MUCH!

NNRNN

NXXXN
RXPXR
NXXXN
NNRNN
N = No Attack, might be wrong as Reach is a bit iffy
R = Reach only
X = Attacker
P = PC
Corners do count.
Also see Flanking.

Not quite sure what you are trying to represent?

If trying to show which squares a medium or small character with a reach weapon threatens, it would be:
YYYYY
YNNNY
YNRNY
YNNNY
YYYYY

Y is where the reach user can attack or take AoOs, N is where he cannot attack with the reach weapon, R is where he is located.

There is no maximum limit on the number of attacks that can be directed at a single target.

Considering only enemies with a five foot reach who are on the ground, there are eight adjacent squares to the surrounded target. All eight can attack with however many attacks they are entitled to.
You could even add a ring of 16 enemies with reach weapons. The target will have a cover bonus because of the adjacent attackers, but all 16 of the reach weapon armed enemies can attack as well.

WARNING: BAD ASCII ART

R.R.R.R.R
R.A.A.A.R
R.A.X.A.R
R.A.A.A.R
R.R.R.R.R

There is a feat which will get rid of that negative for attacking over their allies with reach weapons too, if you are really wanting to hit this guy with 24 attacks in a round. To add to this there is a much larger number of squares that you could pack with ranged attackers around this one, and then an even larger square around that one you could fill with various sniper archetypes.

Here is clarification from the CRB section on combat:

"Threatened Squares: You threaten all squares into which you can make a melee attack, even when it is not your turn. Generally, that means everything in all squares adjacent to your space (including diagonally)."

And reach weapons DO get the second diagonal, as a specific exception to the 'two diagonals are 15 feet' rule. SlimGauge's Mr X in his ASCII diagram is in what is technically known as a 'poor tactical position' if all those As have weapons and the Rs are reach whackers. (And now I'm imagining a pack of whip wielders at 15' just to add insults to injuries.)

And reach weapons DO get the second diagonal, as a specific exception to the 'two diagonals are 15 feet' rule. SlimGauge's Mr X in his ASCII diagram is in what is technically known as a 'poor tactical position' if all those As have weapons and the Rs are reach whackers. (And now I'm imagining a pack of whip wielders at 15' just to add insults to injuries.)

Also forgot: EVERYONE there is enjoying flanking bonuses too. Paizo isn't that clear on how it can get in some reach situations, but this one's pretty clear-cut, as everyone has a partner directly opposite no matter the angle. Stab away!