I would imagine that a printer that does all three would look like something in a Rube Goldberg cartoon.
Imagine something
like this, with a laminator bolted on the front. Now add in all the problems you're going to have trying to laminate (a continuous process) while the printer is still running, doing its printing and cutting (an intermittent process).
Separate machines are the way to go. Not only will it be likely less expensive, less problematic, but as your shop expands you can easily add capacity by identifying the bottlenecks. Most shops will have multiple printers per one laminator. A single Zund flatbed cutter is also able to keep up with around 4 normal solvent printers -- I only mention Zund since you are interested in die-style cutting, and a normal plotter is only going to be able to do kiss-cutting at best.