MrCool recently came out with a DIY version that has a ceiling cassette instead of the wall mounted air handler. We have a detached space from the house that needs A/C since the crappy little wall unit has died. The small is also not ideal for a large wall mounted air handler.

Previous owners cut every corner imaginable and the distance between the ceiling joists is 20" instead of 16". The installation manual says the cassette fits in between joists that are 16" on center and my space is wider. Is there any issue with sistering some 2X4s to the existing joists so that I can install the cassette into the ceiling?

If you haven't seen their ceiling offering, it's longer than it is wide, like the wall cassettes, so it wouldn't fit like you describe.

OP - no issue sistering on some blocking. Assuming you have attic access, you might add some blocking/bridging to the adjacent joists just to tighten everything up.

Weird,... I guess it must let them share more parts with the wall mount units.

If you're going to do it, I would try to make sure that the screws you use always go all the way to the joist (i.e. if you end up using 2 piece of wood, don't just screw one to the joist and the second to the first.)