I'm planning to develop a web application in CakePHP that shows information in graphics and cards. I chose CakePHP because the information that we need to show is very structured, so the model approach makes easier to manage data; also I have some experience with MVC from ASP.NET and I like how simple is to use the routing.
So, my problem is that the multiple organizations that could use the app would have their own database with a different schema that the one we need. I can't just set their string connection in the app.php file because their database won't match my model.

And the organization datasource couldn't fit my model for a lot of reasons: the tables don't have the same name, the schema is different, the fields of my entity are in separated tables, maybe they have the info in different databases or also in different DBMS!
I want to know if there's a way to make an interface that achieves this

In such a way that cakephp Model/Entity can use data regardless of the source. Do you have any suggestions of how to do that? Does CakePHP have an option to make this possible? Should I use PHP with some kind of markup language like JSON or XML? Maybe MySQL has an utility to transform data from different sources into a view and I can make CakePHP use the view instead of the table? In case you have an answer be as detailed as you can.
This other options are possible if it's impossible to make the interface: - Usw another framework that can handle this easier and has the features I mentioned above. - Make the organization change their database so it matches my model (I don't like this one, and probably they won't do it). - Transfer the data in the application own database.
Additional information: The data shown in graphics are from students in university. Any university has its own database with their own structure and applications using the db, that's why isn't that easy to change structure. I just want to make it as easy as possible to any school to configure their own db.
EDIT: The version is CakePHP 3.2. An important appointment is that it doesn't need all CRUD operations, only "reading". Hope that makes the solution easier.
I don't think your "question" can be answered properly, it doesn't contain enough information, not enough details. I guess there is something that will stay the same for all organizations but their data and business logic will be different. But I'll try it.
Model is a whole layer, so if you have completely different table schemas your business logic, which is part of that layer, will be different as well. Simply changing the database connection alone won't help you then. The data needs to be shown in the views as well and the views must be different as well then.
So what you could try to do and what your 2nd image shows is, that you implement a layer that contains interfaces and base classes. Then create a Cake plugin for each of the organizations that uses these interfaces and base classes and write some code that will conditionally use the plugin depending on whatever criteria (guess domain or sub-domain) is checked. You will have to define the intermediate interfaces in a way that you can access any organization the same way on the API level.
And one technical thing: You can define the connection of a table object in the model layer. Any entity knows about it's origin but you should not implement business logic inside an entity nor change the connection through an entity.
If that's true either use the CRUD plugin (yes, you can use only the R part of it) or write some code, like a class that describes the organization and will be used to create your table objects and views on the fly.
Overall it's a pretty interesting problem but IMHO to broad for a simple answer or solution that can be given here. I think this would require some discussion and analysis to find the best solution. If you're interested in consulting you can contact me, check my profile.