I doubt this is possible, but there's no harm in asking, right?

In "Standoff", you run between consoles trying to solve a puzzle. As you uncover more clues, more branching options become available.

Is there some way to do that in the Foundry?

You can place popup dialog on your map and under the states keep it hidden until object complete. The object could be anything. You could also use marker reached. The popup on your map won't appear in the story line.

Yes, you can do that. It has to be a map dialogue though, or a default text on a contact. You can have more dialogue buttons appear based off of component complete state. Default text is probably the way to go, if possible, because you can interact with a contact multiple times vs just once for a dialogue (it will be minimized on the player's screen if you use the failed state, but that is a bit clunky).

It cannot be a dialogue that's part of the storyline or a talk to contact that is part of the storyline. However you can easily make a pseudo objective using those tools that is not actually part of the mission plot line.

Wow...this looks so much like my recent problem...

I implemented something similar in my mission, "Komahashi Maru", where the player has to complete several tasks before they are able to bring down a forcefield that was locking them in Cargo Bay 2. I used a single NPC, Commander Rem Brott, to help the player keep track of the tasks they still need to complete.

This was achieved by giving Rem Brott a default prompt. Each dialog branch is associated with a specific task. So if there are 6 tasks, there will be 6 dialog branches. As the task becomes active, the associated dialog branch becomes visible and when the player completes the task, that dialog branch becomes invisible. I thought it worked out quite well and is an intuitive way to help the player keep track of the tasks.

Yeah, you can do this best with npc default dialogues hidden in objects. That way they can be talked to over and over again, and depending on what you do with triggers, they will say different things or give different options with dialog prompt triggers.

I do this with npcs in branching dialogue part 2. There are naughty tribbles.

Thanks for the help! I will implement them immediately.

I have a default dialogue with several buttons set to become hidden on This Component Complete. I only want that branch to be taken once. Its not working. Everytime I interact with the object all the butons are there. Any suggestions?

I don't think This Component Complete works with buttons. You need to use Dialogue Prompt Reached. Unfortunately, Dialogue Prompt Reached currently doesn't allow you to select Default Text. Instead you'll have to use a map dialogue.

If it's a person you want the player to talk to just place an invisible object 10 feet as the trigger for the dialogue, and set the interact duration to instant.

Then with the map dialogue you can select the text box of each branch and use that to hide the button for that branch.

Thanks, that's what I concluded. So we are still back to invis objs.
The problem with a map dialogue is everyone in the mission sees it on their screen. I just want the person interacting with the dialogue to see it.