Multiple buttons to one interrupt pin

I am getting ready to start a project that will be battery powered and make use of the Watchdog Timer. I would like to have 4 user input buttons, but I am facing the limit of 2 interrupt pins on the UNO that can bring the device out of SLEEP_MODE_PWR_DOWN.

I had a thought about wiring all buttons to a single interrupt pin as well as to individual input pins which would allow any pin to wake the device up. I'm stuck figuring out if it's electrically possible to do this in such a way that the software could differentiate which button was pressed without the HIGH state (or in my case a LOW because I'm using INPUT_PULLUP) being present on all pins. Can a few resistors help here or is there another approach that might accomplish the same goal?

I'm not sure if this is even a possibility... But I'm trying to learn.

My backup plan would be to have the 4 buttons only go to their respective input pins, and add a button tied just to the interrupt which must be pressed prior to any user input so it can wake up for a set period of time ready to receive input.

Thanks!

Use 4 buttons to four normal digital inputs. And use 4 diodes from the interrupt pin to the four buttons. Every button pulls the interrupt low via a diode. In the sketch, read the 4 normal digital input to check which button was pressed.

Thanks! After some reading I now know 100% more than I used to about diodes!