Shopify allows each product to have up to 3 options and no more than 100 variants. If you want to go beyond this limit, you can use a 3rd-party app like Product Options Variant Option.
Our app brings you the ability to create unlimited custom options and variants for your products, satisfying all your needs for strategic sales and personalized aesthetics.
You add variants to a product that comes in more than one option, such as size or color. Each combination of options for a product is a variant for that product.
For example, suppose that you sell T-shirts with two options: size and color. The size option has three values: small, medium, and large. The color option has two values: blue and green. One specific variant from these options is a small/ blue T-shirt.
You can see a list of variants for a product on its product details page.
Further details can be found in this Shopify document about Variant
