Search Objects with by associated tags?

Call out to @NigelG as I’ve seen some great answers to related questions!

I have a company database where each company has a list of “categories” that they fall into.

Based on some other posts I’ve seen on database structure I have the following:

Data Type:

Startup

Field Types:
Categories (List of Categorys)
Description (Text)
Logo (Image)
Name (Text)
Site (Text)

Data Type:

Category

Field Type:

Partners (List of Startups)
Main Category (Text)
Subtopic (Text)

My question is, how do I do a search for startups across all of the field types for display in a repeating group? I am using the search and autocorrect plugin but it seems that this will not work with my “Categories” field type.

I’d like the user to be able to type in a company name or keywords that may be in the description or list of categories and get all of the relevant results.

Any help here is greatly appreciated!