Is it possible to set up a complaints tracking database with SugarCRM?
This is certainly possible. The way I would approach it is to create a module called "Complaints" using Module Builder. Then you can create a "complaint" record every time one is filed. If you build a relationship to another module like Accounts, then you can relate these records. That way, you can see what complaints came from what organization. You could probably also just use the existing "Bugs" or "Cases" module but if you plan on using those, creating a new one would be the best bet.
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