Yes, if you responded to a US office action but your trademark application was still refused, you can appeal the examiner's decision to the Trademark Trial and Appeal Board( TTAB). The TTAB is an administrative tribunal that reviews trademark cases, including appeals from denied trademark applications.
The appeal process to the TTAB involves filing a Notice of Appeal, paying a required fee, and presenting arguments and evidence in a formal legal proceeding. The TTAB will then issue a decision on the case.
Keep in mind that appealing to the TTAB involves a more formal legal process, often requiring legal representation, and can be a lengthier and more complex procedure than responding to an office action.