Yes, it can handle this easily. You have 32 inputs.
If I read your question correctly, you want 4-players and 2-inputs each - That's 24 inputs. Plus your 4 coin and start inputs gives you 32 inputs used. You want to add 4 extra buttons for player 1 and 2, but these could share with the P3 and P4 joystick inputs, so no problem there.
If you get more ambitiuous - The KeyWiz supports 32 inputs, so 4-player 4-button games are possible, but you would need to hack a gamepad for the coin, start, and admin (pause/escape) buttons.
I like a dedicated Escape button and Pause button, but you can also wire the KeyWiz so a single button press activates a shifted input using adapters that RandyT sells.
My personal desktop controller plans have the KeyWiz able to play 4-player 3-button games (28 inputs), with Pause and Escape (now up to 30) dedicated 7-button layout (32 inputs) and shifted buttons for Coin and Start, so a total of 40 inputs out of a 32-input encoder.