At a special meeting, you can do almost everything that you can do at a regular meeting, unless your local code or rules say otherwise (with the exception of towns, which may not pass a resolution or order for the payment of money at any other than a regular meeting. See RCW 35.27.270).
But, RCW 42.30.080(3) says that you cannot take “final disposition” on an item that was not posted on the on the special meeting agenda. While “final disposition” is not defined in the statute, RCW 42.30.020(3) defines "final action" as a collective positive or negative decision, or an actual vote “upon a motion, proposal, resolution, order, or ordinance.”
Therefore, you cannot vote on or take a “straw poll” on a new matter brought to the table in a special meeting. Why? Because “final action” includes any collective decision on a “motion, proposal, resolution, order, or ordinance” and final action cannot be taken on a matter not listed on the original agenda.
So, can a governing body give “interim guidance” to the executive or staff such as asking the executive or staff to provide additional information, on a matter that was added to the agenda of a special meeting? Probably not. The better practice is for each member of the governing body to express their concerns during the meeting and staff can then decide what needs to be done to bring the item back to another meeting.
However, at a special meeting you can amend the agenda to discuss something not on the original agenda and go into executive or closed session (if appropriate) to discuss something not on the original agenda.
Some actions such as granting franchises cannot be adopted until a specific amount of time has passed after introduction. See RCW 35.23.251 for second class cities, RCW 35.27.330 for towns, RCW 35.17.220 for cities operating under the commission form of government, and RCW 35A.47.040 for code cities. RCW 36.55.040 and RCW 80.32.010 deal with franchises in counties. So, if you introduce a franchise agreement at a special meeting you can discuss it but cannot adopt it at the same meeting.