There is no implied limit to the number of stocks you can short with IBKR. The limit will be established based on the funds available in your account that allow you to meet the margin requirements to short a stock.
Is there a limit on the number of stocks I can short?
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What is the margin requirement for shorting stocks?
Is it possible to disable naked short selling as a precaution?
Is there a way to set risk limits for an account?
How many FHSA can I have?