The closest native option I know of is to create an "ask the user" report (see here for details:
https://help.quickbase.com/user-assistance/selection_criteria_prompt.html), and build your SEARCH button to access the report's URL with the selection values inserted into the search terms.
i.e. I grabbed a copy of the ABC Project Manager 3 app from the Exchange, then created a new report on the Tasks table with a single filter stating "Task Name is equal to <ask the user>", then saved the report. If I search for the term "Prototype" the URL generated is
https://team.quickbase.com/db/bpfewjcn2?a=q&qid=59&nv=1&v0=Prototype. The nv=1 indicates how many search terms there are for the report, and the v0= and subsequent v1=, v2=, etc. if there are additional search terms correspond to each search field.
You could build a formula URL button to display your multiple choice values like this: URLRoot() & "db/" & Dbid() & "?a=q&qid=YY&nv=ZZ&v0=" & [MultipleChoiceField1] & "&v1=" & [MultipleChoiceField2] & "&v2=" & [MultipleChoiceField3] and so on, with YY being your report number and ZZ being the number of search terms you have.
