How do I know how many models I would need to solve a problem?

I'm starting out in my Machine Learning journey and a possible aha moment (or very possibly a wrong turn) is how to think about how a model fits into my application. So right now I have an application that analyzes documents using regex and pulls out pieces of information using patterns... as you can guess, this is an endless cycle of adding new regexes or adjusting them based on someone typing a piece of data a little bit differently into their document. So my question is... if I were to do this with ML... would I have a model for each piece of data I was pulling out? Let's say I wanted all the locations mentioned and all the dates. Would I have a model that is trained to recognize locations and another one trained on dates and simply throw the document at both? Would love to hear how others use ML models in their web applications.