Tasting out new flavors

A new ice cream parlor has 4 flavors: Vanilla, Chocolate, Strawberry, and Butterscotch. They want to give 4 customers (Alice, Bob, Carol, and David) free samples of their ice creams to get feedback under the following constraints:

• They want each customer to taste 2 flavors.
• They want each flavor to have been tasted by 2 customers.

For example, here is one way they could achieve this:

But what if the parlor came up with 7 flavors and 7 customers? Suppose they wanted

• each customer to taste 3 flavors;
• each flavor to have been tasted by 3 customers.

Would it still be possible?