How to make Flat Rate Shipping have a max amount of items?

I'm using the Flat Rate shipping on my site, set to $20, but I want to make it so you can only ship say 5 items for $20. If the user has 8 items, it would double the shipping charge and charge $40, is that possible?

Use zone shipping instead and create a zone that encompasses your entire shipping area for the "flat rate." With the zone rates you can specify maximum products quantities for each shipping rate.

Zone 1 Shipping Table
Shipping rates to Zone 1 destinations based on a group of maximum order weights/prices. Example: 3:8.50,7:10.50,... Weight/Price less than or equal to 3 would cost 8.50 for Zone 1 destinations.
You can end the last amount as 10000:7% to charge 7% of the Order Total