This is an example of how you can set your variants using the Shopify platform. Maximum 3 options, maximum 100 combinations.

This product page shows a t-shirt that comes in 3 different sizes, 3 different colours and you can choose whether to add some custom text (2 options: customised yes or no). 3 sizes x 3 colours x 2 customisation options = 18 combinations. 

A phone case available for 7 different models in 8 different colours with a choice of 3 designs would give 7 x 8 x 3 = 168 combinations. 

You have 2 choices for products with over 100 variant options: 

1. Split the product into smaller combinations
2. Third party apps

Free plan available with Variants Option Product Option and Infinite Product Options. 
Paid apps available include Infinite Options, Bold Product Options and Product Options and Customizer.

See this page for more details on third party apps including "free plan available" and support options.