You can do so by creating a custom coordinate system and then specifying the desired unit (US Foot, for this example), then creating a grid-based on custom coordinate system. In this example, a grid with NAD83/UTM zone 17N (metres) coordinate system is created in the blue color. Another grid with a NAD83/UTM zone 17N (USFoot) custom coordinate system is created with an orange color.
Likewise, you can create multiple sets of measured grids with different coordinate systems in one MAP View (e.g. one set with NAD83 UTM, another with NAD27 UTM, another with some other local coordinate system) without the need to transform the MAP View.