Many articles and books that discuss productivity of meetings suggest that a meeting should have both a goal and an agenda as a prerequisite for starting the meeting.

While I am perfectly happy with this rule and I am certain it applies to the majority of meetings I can argue that once in a while there're meetings/discussions for which figuring out a goal would be as good as starting the meeting and having an agenda is almost pointless as the initial agenda is unlikely to be followed once participants discover more about their goal.

For example - think about a meeting with another team to discuss integrating two products or components of a product. The goal could be - to agree on interface for this integration and the agenda could be
1. Introductions
2. Team A (frond end team) presents the information that they believe they need
3. Team B (back end team) evaluates the requirement and suggests a solution
4. Teams generate ideas and discuss options
5. Any actions are reviewed and owners assigned

Easy, right? It is even easier if it is a recurring meeting when the goal is usually well understood and you can refine the agenda to ensure current requirements are met.

Now consider the following scenario - a new requirement is introduced by the business which would mean changes across components and domains and would potentially affect a few or perhaps all teams. Team members voice concerns and suggest a meeting to decide how to proceed. There's numerous concerns  some very specific and some too vague.

When faced with similar scenario recently I have decided that the goal to "decide how to proceed" is too vague and I suspected there's several more specific goals that can be more useful but wasn't sure what they are and consulting almost 30 team members about that would in effect mean starting the meeting earlier (and probably making people unhappy that they are being interrupted). Due to my expectation to see many different goals I also thought the agenda will drastically change and depend on which goal is most important.
So I decided to start the meeting by inviting everyone to state their goal and recorded the goals on a white board. I then read all the goals and asked the team to indicate which 3 goals are the most important to them. Finally I counted the votes and identified the 3 goals with most votes. I then suggested that we should spend a fixed amount of time (e.g. 10 minutes) discussing the first goal. At this point I did not really have much of a plan rather than hoping that the team can generate it or else some obvious actions may come out of discussing the top 3 goals.
In this instance the team did have very good suggestions, with very little participation on my side generated the next points on the agenda and with some minimal time managing intervention we managed to complete the meeting on time, do a re-cap at the end that suggested almost 100% of the participants were satisfied with the result.

So here's in summary the approach for the meeting without agenda and vaguely stated goal:

0. Explain to the best of your knowledge why are you having the meeting and state the suggested time slot - e.g. 1hr
1. Explain why there is no goal and ask everyone (best to go around the circle) to state their goal for the meeting
2. Record all the goals on a white board (try grouping where necessary)
3. Read the goals so that everyone can hear them and allow some clarification questions where necessary
4. Ask the team to pick their top 3 goals
5. Count the votes and announce the first goal to discuss
6. Time box the discussion and let/ask the team to make suggestions of how to proceed

From here on the meeting may take different from from what you or the rest of the team expect.
Some tips that will help you:
7. Remember to time box any discussions and ensure they do not overrun
8. Ensure the group is happy with any statements made by individuals rather than changing direction every time a new suggestion is made
9. If the group is big or if people are interrupting each other and fail to progress because of that introduce a talking token (e.g. only the person holding the token can talk and if someone wants to talk should ask for the token)
10. Ensure the meeting ends on time unless everyone agrees to extend it (sometimes this might be more valuable than finishing on time)
11. Before the meeting ends ask for a re-cap so that everyone hears everyone else's position. This might indicate if another meeting like this is required or more specific actions have already been generated and the group is happy to close the discussion.
12. And finally remember that you own the process not the content - trying to participate will damage your ability to time manage, spot actions items or introduce new rules when necessary (e.g. the talking token)

Well I hope the suggestion could be useful if you face similar situations. Good luck :-)