Unfortunately no. To do what you want, you could create another table that has the options, then use a ‘Link to Other Table’ type for your column. Then you could dynamically add to the table that is being referenced.
When creating or updating records, if the choice string does not exactly match an existing option, the request will fail with an INVALID_MULTIPLE_CHOICE_OPTIONS error unless the typecast parameter is enabled. If typecast is enabled, a new choice will be created if one does not exactly match.