Yes, you can create as many watchlists as you like in the Quant Investing stock screener.
You can even have the watchlists emailed to you in the form of an Excel spreadsheet.
These articles show you exactly how to do it:
How to create and edit Watchlists in the Quant Investing stock screener
How to get your new stock screener ideas and Watchlists by email
How to track your portfolio with automatic updates of closing prices and ratios
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