Howdy dsweise,
I can see where you are coming from, would definitely be useful on one hand to show a few upcoming weeks regardless of the date.
To answer your question yes it is possible to alter the query and show more weeks. But is it easy? Not even a little. To modify that you would need a combination of theme overrides, and a lot of custom code to keep looping the calendar grid paste the end of the month. Further a bit more custom vote to alter the WP_Query for Month Views so that it includes more future events. Finally probably going to need a decent bit of CSS as well to get it to behave how you’d expect. All in all, a sizable project for your or a freelancer to tackle.
Does that all make sense? Does that fully answer your question? Please let me know.
Cheers!
– Brook