If you've already done this on 3 separate forms, then combining them into 1 form should be pretty easy. It sounds like it's more a matter of just HTML adjustments and scripting merging, then anything more complicated.
I'm assuming you're providing this search functionality on a website. Can you add HTML tags "select/option" to your input form to choose which of the 3 search features?
Then, in your back-end script, you receive that selection and run the proper set of API calling code you've already written.
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