Yes, indeed, you will use multiple satellite images most of the time, if not always. Consider that space-borne instruments typically acquire images in different spectral bands separately. In order to properly interpret those data, you need to analyze these images together. Furthermore, if you happen to use a multi-directional and multi-spectral instrument like NASA's MISR, you will automatically have access to 36 images for each location of interest: 4 spectral images from each of 9 different cameras. In addition, it is customary to accumulate multiple images of the same location in time to document the temporal evolution of the system under observation. And depending on your particular application, you may need to reply on frequent imagery obtained at a reduced spatial resolution, combined with occasional images at a much higher spatial resolution. You might even consider acquiring images in entirely different spectral ranges (solar, thermal, microwave) in some cases. In summary, it is nowadays fairly rare to use a single satellite image in any given application.
Of course you can use, however; you may follow some processes depending on your purpose for example; if you want to do a post classification change detection analyses. You need standart spatial resolutions, you can modify the all sensor's resolution to the highest spatial one etc...
There is always a need of accuracy assessment, so using two images of different satellites with different resolutions can be used for the purpose, but the projection has to be same for both.