phil-lee has the right idea but the unit with the problem is the Coin unit. The wiper side looks like this:

pasted_image (resized).png

I’ll bet it’s that limit switch. It’s supposed to open at the fourth position I’ll bet it’s bent slightly and opening early.

If you look in the bottom of the cabinet there is a stepper called the coin unit.... on the one side will be the spider on the other side with the coils you’ll see a switch that opens when the gear turns around it should only open in the fourth position.

Here is a Williams coin unit in reset position. In this position, you’ve pressed the credit button once. The 1 player lite on the back glass is lighted. The switch with the arrow is closed.
Coin Unit WMS (resized).jpg
When you press once again the credit button, the coin unit advances one step. The 1 player lite on the back glass goes off, 2 players goes on. The switch is closed.
Third time you press the credit button, the coin unit advances one more step. The 2 players lite on the back glass goes off, 3 players lite goes on. The switch is still closed.
Fourth time you press the credit button, the coin unit advances one last step. The 3 players lite on the back glass goes off, 4 players lite goes on. The switch with the arrow now opens.
In your case, the switch probably opens when you’ve pressed de credit button 3 times. Because of this, you cannot add a 4th player.

Adjusting this contact should solve your problem…