Shared short codes are not permitted in the US and Canada or in most countries worldwide.
The only (very narrow) exception to the prohibition on shared short codes that is permitted by US/Canada carriers is a short code that sends OTP (one-time passwords) or authentication codes with strict adherence to a template, and no option for customization by the brands that are sharing the short code.
Problem with that is there may be other services that also leverage the same short code, meaning you may be blocking something you need in the future.
Edit: apparently according to Twilio: