I see, he wants to use the row/column multiplexing method, but that has issues with the daisy chained LEDs in the LED blocks. You could drive each of those as separate LEDs more easily. I think that means the three rows of four blocks become 48 LEDs plus the 11 single LEDs for 59 total. BTW, they are not all independent. The four in a block are all lit together and the last LED in any row is only on when the others are also lit, etc.
One advantage of multiplexing is that you can use fewer constant current drivers. 16 outputs can control up to 64 LEDs, 8 high side drivers and
8 low side constant current drivers. The blocks should all work with the same current so you can use 6 constant current drivers for those. The 11 singles can use two constant current drivers for those. If you want to get really fancy you can use 8 DACs (one chip) to drive the constant current transistors and have software defined brightness which can provide very even control of the brightness and other features like night time dimming.BUT.... this will require real time control by the rPi, not once per minute updates. I looked at using the rPi for reading ADCs over the SPI bus and it is not well suited for real time work, especially if it will be doing other stuff. Given the limited benefit of multiplexing for your design I would suggest that you stick with direct drive.
If you want to use the multiplexing scheme which does have the advantage of requiring fewer drivers, I would recommend using an MCU to do the multiplexing and let it talk to the rPi by I2C or RS-232. Using RS-232 makes it easily adaptable to any PC as well. That becomes one "smart" chip and 16 transistors. Not too bad.