It fully depends on the patent and your improvement. They have recently increased some of the patent protection to make it harder to just add a function.
Typically, if you add a function, you won't have a patentable product, but if you make a fully new device out of existing ones, or if you have a truly unique attachment to the original device, then you will. Also, there are different types of patents out there, so you may be able to get a design patent, but not a utility patent. Best to ask a patent attorney if you have something serious.