LCD or CRT monitors that use the analog video input will support 32 bit color, 64 bit color 128 bit color etc. Theoretically they will accept an infinite number of colors. The bottleneck is the video card and or the digital video interface. On laptops the limitation is determined by the amount of video memory and the digital interface to the LCD screen.
The difference between 24 bit color and 32 bit color is the extra 8 bits in 32bit color are used for the alpha channel (or transparency). 32bit color is arranged in RGBA (more or less), with 8 bits per channel. This means 32bit color has the same color accuracy as 24bit color.