I ended up with a couple of rectangles inside of the "myObject" frame.
But they were not grouped.
Though this partly solves my problem, I'm aware that Indesign won't allow me to do this in UI. (That is, it's only a single object or a group that can be "pasted into"). Am I really in for a big problem if I use this method?
Actually, although the UI won't let you create such an object, it does support them. Objects that start life as Excel charts have exactly this structure. Take them into Illustrator then copy and paste into InDesign and you'll find you have objects that are exactly what you've discovered.