Variable data is only one-way in Illustrator is when looking to establish a 'live link', that is correct.
Otherwise, variable data can do multiple graphs in the same document but you just have to make sure your individual graph states are in separate .csv (or csv or .txt if using the VariableImporter script).
So if your issue is solved by some automatic process that takes customer data, puts it into individual CSVs and you have a constant 'main' data csv which does not change in regard to its variable names or amount of variables, then this can be a mechanical 'live link'. In such a setup various automation scripts would do this work every time you want to update the data and not go through a lot of manual clicking.
- Turn customer data sheet into separate .csv files for the graph variables in Illustrator.
- Have your Illustrator document already contain bound graphs to named variables, these are items in your 'main' data csv so for each graph you have a file path like an image path.
- Use a scripting command to import the same 'main' data csv that has all the items unchanged in it.
- When it imports, since the variables already are bound and nothing changed in your main csv (regarding variable names and quantities), it will just go through all the graphs and update the graph as it is referenced by file path like an image file.
- So now you should have all your graphs looking new.
The above process could be made into a one-click operation but still it's a very mechanical DIY-style 'weekend at Bernie's' 'live-link'. To go the next step it may be possible to automatically invoke this process when opening an Illustrator file. To do something when a document is being opened it may be possible to leverage CEP extensions as they are reportedly endowed in Illustrator with the ability to listen to an event which happens when a document is being opened.
If such an extension can indeed listen to this event (some Adobe apps have different support for such events), this process can be invoked when a document is opened by a user or by the application (opens multiple files, or file was double clicked from file system, or a script opened a file). However as this process may take a bit of time, I am not sure what will happen when multiple files are opened like this - but in any case you would want to verify the last time the user updated their sheet with the last import time so your process doesn't have to repeat work that will not change anything.
Another way could be using AutoHotKey on Windows or Keyboard Maestro on Mac to also listen in to Ctrl+O key combo while inside Illustrator. Theoretically this will help if you want your process to only work when a file is opened using Ctrl+O.
Also for inspiration, check out this link!
https://www.linkedin.com/pulse/illustrator-power-user-interviews-multiple-variable-graphs-hall/