Any color shirt can go with a taupe suit although jewel tones, earth tones and pastels look best. The contrast between taupe and bright colors or black can be too strong, and shades of brown or other neutrals can appear overly washed out.
Taupe and other light suits are more appropriate to summer and spring wear, so lighter and bolder shirts are a pleasant complement. Dots, stripes and other prints also work with taupe suits either in subtle or bold patters. Taupe can have undertones of yellow or olive, so be careful if using yellow or greens that attention is paid to these undertones. Yellow stripes in a tie could highlight a yellow undertone, for example, but with a paired lavender shirt, one could look more like an Easter egg than stylish.