Should websites provide high contrast or alternate schemes?

With regards to Accessibility, many sites focus on font-size adjustments either the browser's / OS's native controls or via a control on the page (usually denoted by 3 capital A's of varying size).

However, there are some instances where a contrast adjustment may be needed. Webpages can be affected by the OS's high contrast mode (mentioned here with screen shot); however, depending on the stylesheet, this may end up being a mess.

Because of this, should websites that have higher accessibility requirements provide options for the visitor to select a style / color scheme that provides a higher contrast than the default? If so, should there be varying degrees or just normal and the extreme high contrast mode that's look like the OS's version?