Multiple keys at once

I'm using SDL to detect if keyboard keys are pressed or released. It appears to be able to detect some combinations of multiple keys pressed at the same time, but a lot of combinations of more than 3 keys don't work. That's quite annoying, because I'm using letters from the keyboard as an octave from the piano and this means not all combinations of multiple notes are working. Is there a way with SDL to detect even those combinations that don't work? Or is this a hardware thing in the internal circuitry of the keyboard?