I think what you're looking for is something like this:

boolean[] gameState;
int numStates = 3;

public void setup()
{
    size(600, 600);
    background(0);
    gameState = new boolean[numStates];
    for (int i = 0; i < numStates; i++) {
        gameState[i] = false;
    }
}
public void keyPressed()
{
    if (key == 'm')
        gameState[0] = true;
    else if (key == 'k')
        gameState[1] = true;
    else if (key == 'q')
        gameState[2] = true;
}
public void keyReleased()
{
    if (key == 'm')
        gameState[0] = false;
    else if (key == 'k')
        gameState[1] = false;
    else if (key == 'q')
        gameState[2] = false;
}


This way you can store multiple states simultaneously and test them by comparing to the gameState array with the index you'd like to test. For multiple key presses you can use a counter variable and simply increment it when the key is pressed.
Hope this helps!

Another way could to check the gamestate within keyPressed and have different logic for each key based on the state. 

If you use a switch structure within the keyPressed method, you could use the default option to set the initial state and then use the cases to handle the second press.  This would assume that there will always be a second key press, but you could always handle resetting the state on a timer or similar elsewhere if needed.

Pseudocode:

1. void keyPressed()
2. {
3.       switch (gamestate)
4.       {
5.             case State1:
6.                   if key = m
7.                         //do something for m, m
   
8.                   else if key = k
9.                         //do something for m, k
   
10.                   gamestate = null;
    
11.             case State2:
12.                   if key = m
13.                         //do something for k, m
    
14.                   else if key = k
15.                         //do something for k, k
    
16.                   gamestate = null;
    
17.             default:
18.                   if key = m
19.                         gamestate = State1;
20.                   else if key = k
21.                         gamestate = State2;
    
22.       }
    
23. }
    

Thanks for both of your responses it definitely helped it make more sense. Here is what I have now and the program runs great. The only issue is nothing happens until two keys are pressed.. So for example when m is pressed once the background should turn white. If m is pressed and then k is pressed the background should be white with an ellipse(200, 200, 50, 50);

Eventually this program will be with audio so when m is pressed an audio track will play and once it's done you'll select another audio track while in the first state chosen. Like a choose your own adventure audio program.

Here's the code:

1. int gameState = 0;
   
   
   void setup() {
    size(600, 600);
    background(0);
   }
   
   void draw() {
    smooth();
    
   }
   
   void keyPressed() {
    switch(gameState) {
     case 1:
      background(255);
       if (key == 'm') {
        // do something for m, m
       ellipse(50, 50, 30, 30);
       } else if (key == 'k') {
        // do something for m, k
       ellipse(200, 200, 50, 50);
       } else if (key == 'q') {
        // do something for m, q
       rect(40, 40, 10, 20);
       //gameState = null;
       }
       break;
   
      case 2:
       background(255, 0, 0);
        if (key == 'm') {
         // do something for k, m
        ellipse(90, 90, 10, 10);
        } else if (key == 'k') {
         // do something for k, k
        ellipse(40, 40, 15, 30);
        } else if (key == 'q') {
         // do something for k, q
        ellipse(200, 200, 60, 70);
        //gameState = null;
        }
        break;
       
       case 3:
        background(0, 255, 0);
         if (key == 'm') {
          // do something for q, m
         rect(80, 80, 10, 40);
         } else if (key == 'k') {
          // do something for q, k
         rect(30, 30, 40, 70);
         } else if (key == 'q') {
          // do something for q, q
         rect(300, 300, 60, 60);
         //gameState = null;
         }
         break;
        
        default:
         if (key == 'm') {
          gameState = 1;
         } else if (key == 'k') {
          gameState = 2;
         } else if (key == 'q') {
          gameState = 3;
         }
         break;
    }
   }
   

I know you said it would always assume there's a second key press so excuse my lack of knowledge here.

You can put the call to smooth() in the setup method, rather than calling it on every frame from draw().

The first time you press a key nothing will happen because the gameState variable is 0 and there is no "case 0:" section of the switch statement. It will fall through to the default case, which then sets gameState to 1, 2, or 3. So the next time you press a key you will get some result.

I also changed my code above to initialize the array in a way that processing seems happier with, if it was giving you an error. If the switch statement makes more sense to you though, go with that.

I think the switch statement will work better for my end result it's just this tiny little hiccup of nothing happening the first time a key is pressed. When I hit m once it is showing that it's now inside the 1st case which is perfect, but again nothing happens until the key is pressed again or the k or q key is pressed. If I set the gameState variable to 1 then it will always go into the first case which isn't ideal either. Just wondering if there's an easy fix to that or if I should just try a different method.

1. default:
   if (key == 'm') {
               gameState = 1;
2.             //Do something for first m press
         } else if (key == 'k') {
               gameState = 2;
3.             //Do something for first k press
4.       } else if (key == 'q') {
               gameState = 3;
5.             //Do something for first q press
6.       }

My comment about always assuming a second key press was really referring to that there was no way to cancel - so for example you can't go from one gameState to another without having to go through the second key press.

I can't believe that's the one solution I didn't think of.. I feel silly. As for the second key press thing that's totally fine because once they're in a state for the purpose of my installation there's no need to restart or go into another one so it works great.

Thank you both for your help, I wouldn't have gotten this far this fast without it. Really appreciated!