Can I improve a product that already has a patent?

Yes, you might be able to do that - as long as your invention is (1) novel (2) useful and (3) not obvious. US Patent law permits the patenting of inventions for "any new and useful process, machine, manufacture or composition of matter, or any new and useful improvement thereof."

Yes, of course! One of the underlying principles of our patent system is that in exchange for a limited monopoly, patentees must disclose how to make and use their inventions from the disclosure in the patent document itself. This implies that over time the wealth of publicly available knowledge increases. In fact, virtually all newly granted patents are for inventions that improve upon existing products which may or may not already have a related patent. The question now becomes what do you intend to do with your improved product, i.e., "something else"? It is not clear from your statement of the question whether or not you are simply planning on seeking a patent for "something else", or if you wish to make, use and sell "something else". Those are two different inquiries. The first inquiry relates to patentability for "something else". More particularly, the issue is whether "something else" is useful, novel and nonobvious over what others have done in the past (the prior art). If so, you may be entitled to a patent. So, your next steps would be to commission a "novelty" or "patent" search to see what your likelihood of obtaining a patent might be and then filing a patent application if the search is favorable. These are both services for which you should engage a patent attorney or agent. The second inquiry relates to infringement, more particularly whether you can make, use and sell your "something else" without having to take a license from the owner of the "patent" for the "product". It may be the case that your "something else" falls within the claims of that patent or some other patent that has relevant claims reading on "something else". So, a prudent business person would do further investigation, for example, you should consult with a registered patent attorney to perform a "clearance" or "right-to-use" opinion that will give you some confidence that your "something else" does not infringe any valid patent of another. If there is some arguable infringement, you may need to seek a license from the patent owner or risk an infringement lawsuit.

Most patents are improvements on older technology. Some are also applications of scientific principles already applied in one kind of product but then applied to a new kind of product.