TYPO3 8.7 is it possible to output a specific page with multiple url path s

I'm trying to integrate a vue.js application into a typo3 page.

I have a full functional TYPO3 instance where I can create own pages, edit the content and more. Now I want to add an existing vue.js application within this page.

Therefore I created an extension which added all necessary resources (js, css) and added an own content type which controls the integrations and configurations. The content type outputs a vue.js entry point. So far everything works. Smaller vue.js applications works as they should.

Now comes the challenge: When I want to create a more complex application which relies on the router functionality, I run into a problem.

Let's assume, I integrate my application into the page /shop and my application tries to render a product under /shop/product/some-id. This doesn't work. The URL processing is done by TYPO3 (as designed).

I tried to find a solution within the documentation but I'm not sure what I should search. I need a way to output the same page (/shop) regardless the following path. Does someone have a hint?