You are going to need to find a Shopify developer to build this functionality for you, as something like that is definitely not built-in or available as an app.

https://www.shopify.com/developers
https://experts.shopify.com/developers

I've built Shopify sites in the past, and I can vouch for its flexibility as a platform.

That being said, Padraic is right that you most likely will need a developer to build the custom functionality you're after. It sounds like these are all easy enough to manage as categories and add-on products, though, so any half-decent Shopify developer should be able to handle it.

When it comes to platforms that let you customize — as Shopify does — the short answer to "is it possible?" is always, "yes." The qualifier there is whether or not it makes sense within your budget, and whether or not the proposed features will make a big enough impact on your revenue to justify the up-front expenses.

And, of course, the more customized the platform becomes, the more of a hassle and expense maintenance will be. So that's another factor to weigh when making a decision to go custom.

I've worked with hundreds of businesses who needed to strategize their online offerings in similar ways, so if you'd like a fresh set of eyes — whether that's to help outline the requirements for the software or to dig into the pros and cons of platform customization — I'd be happy to discuss. Let me know if you'd like to schedule a 15-minute call to discuss the problem and see if we'd be a good fit.

Good luck!