I believe you can do this via formulas. You'd add a count to the Values, then modify the formula so it looks something like this:
(COUNT([thing you're counting]),[Category you want to group values by])
Then you'd click the category item, and in the pop-up you'd select "Edit Filter". Then you'd select only the particular values you want to group, e.g. "Red", "RED", "red", etc. When finished, the total being displayed should be the combination of all the 'Red' values.
Of course, the downside to this method is you need to repeat these steps for each grouping you want, so it's not very useful if you have a lot of them, or if kinds of groupings frequently change from widget-to-widget (or based on certain other filters). You can re-use certain complex groupings by saving the formula and naming it, which lets you re-use it elsewhere with the same configuration. However, another downside is that if a given formula will resolve to zero based on the other filters in the view, it will still try to show. That is: if you have ten formulas for the ten possible groupings you want, but because of your current filters only 3 of them are non-zero, the other 7 will still show in the view as empty spaces. Not ideal 😕
Another downside is that, because this is a formula, it only applies to "values". You can't use this method if you want to do something similar for a row or column. This limits the design of your widgets in certain ways. Since you're having to use multiple values, you also lose certain features like filtering by top N or sorting greatest to least.
