The question is a ambiguous as you conflate profile and characterization.
If you are working in the offset world you have two basic choices for colour profiles. First, use a standard profile (GRACOL 2013 ect) for your industry, substrate, and press types. Using industry standard profiles that have been averaged over hundreds of press runs in different conditions makes the most sense and is less costly. The same profile would be used to convert spot and process colours regardless of press type or location. Second, create your own, but with caution. Different substrates can require a unique colour profile depending on their white point, ink set, colour, and printability. Creating your own profile requires advanced knowledge and custom software which can be expensive.
Ideally, each press should have it's own fingerprint/characterization (TVI, gray balance, overprints ect) by substrate if the substrates you use vary enough (Newsprint vs Coated). If you are using an industry standard such as GRACoL then you use the GRACol target specs for the substrate. If you are running two KBA Rapida 105s, for example, you can use one press as a benchmark but with a high degree of caution. Presses are never identical. Presses are more like close cousins than twins and how they print is a reflection of the level of operator training, maintenance, inksets, blankets, fountain solution, and environmental conditions. This is especially true with presses at different locations. Having separate fingerprints/characterizations allows you to make adjustments for each press and substrate combination independently as required. Again, this may not be suitable for all pressrooms. Creating your own specific characterization that is unique to your company is possible but not advisable. It would depend on your circumstances.