In Canvas, how do I require several triggers for a single event?

Easiest way to achieve what your looking to do:

Have your "secret menu items" either on a seperate Canvas, or simply under a seperate hierarchy within your 1 Canvas - for example, you can create a Panel, turn off the Image component of it so the panel isnt seen (or set the alpha color of it to 0), then child all your "secret menu items set 1" to that panel -- basically the point is, you want to group your menus you want to essentially toggle, under different sections of your hierarchy in your Canvas or in a new Canvas completely, but you NEVER want to put Transforms or other things that are not UI elements in your Canvas's because it can mess them up sometimes and not show the children on the UI anymore when visible.

Then, you want to write a script, something along the lines:

 public GameObject[] hiddenMenus;
 
 public void ShowMenuItems(int hiddenMenuIndex){
 hiddenMenu.SetActive(true);
 }
 
 public void HideMenuItems(int hiddenMenuIndex){
 hiddenMenu.SetActive(false);
 }

Now, add a EventTrigger (click on your image you want to act as a "button" basically, click "Add Component", then go to "Event" (or type in the word "event"), then "Event Trigger") -- note youll have to do this one at a time, because EventTrigger doesnt support multi-editing (so you can select all your images and add the component, but you cant do anything with that component to all of them at once)

Then, click "Add New Event" or whatever the button says, and in your case, it sounds like youd want to add a "Pointer Click" event.

Leave the "Runtime only" line alone (this honestly really has no significant difference if you change it, you just dont need to worry about it in this case), then for the empty slot, you want to select the game object, that has this script you wrote on it -- you should really place this script on 1 object, like your main Canvas or your main Camera or something.

Now, set up your array on the object you placed the script on - select the little arrow for the array, give it a number, and then start setting the elements for each index of your array, to the game objects that hold the children of each of your hidden menus -- just remember the index or element number you put them at, so if you named your hidden menus in order by 1, 2, 3, and placed them in your array in that same order, itll be very easy to remember.

Then, go back to your image you want to act as a "button", the last section (the drop down) will become selectable, find your new script you wrote, and select the public function corresponding to what you want that button/image to do when clicked -- in that example, you probably want "ShowMenuItems", then set the number of what will be the 4th field, from 0, to whatever index you setup your menus on - this is where the memory comes in.

Once all that is done, if done correctly, you will be able to show different menus on different images you click on -- then you can apply the "HideMenuItems" as well to hide certain menus when you click on different images if youd so like.

Kind of a long-ish process that can be very confusing at first, but doing it in a "Event Trigger" way for each image, through one script with an array, is the easiest way I can think of doing what you want to do without over complicating the concept too much.

Hope this helped.