You can and some cameras even do it automatically now. With a full single shot of the subject, the resolution you get is at most the maximum of the camera. It is usually slightly lower due to optical imperfection and even many cameras have an anti-alias filter to reduce sharpness slightly in order to avoid moire artifacts.
When you take multiple photos of either the whole image or part then you are gathering more data. These need to be assembled into a higher resolution output which is the principal for panoramic photography. What you get though is not the sum of resolution due to many reasons but you certainly should get more than a single shot.
Images have to overlap so that they can be matched and the common areas blended together. This blending processes the image so that details appear uniform which reduces a little sharpness compared to each shot on its own. Still, just take 4 photos will give you more than double the resolution. For best results, everything has to match between shots, exposure, focus, white-balance and any parameters like tone curve. Modern panorama software can compensate for some differences but this is still processing pixels which results in reduced image quality.
Similar results can also be achieved by taken multiple times the whole subject but with the camera slightly offset between frames. This has the added benefit of capturing more color information since the sensor can be moved to ensure that each color on the Bayer filter is used for all points in the image. This is called Super Resolution and requires processing in order to merge images together. Many mirrorless cameras currently do this.