Bigger Thanksgiving gatherings mean bigger meals—and fuller shopping carts are putting supermarkets to the test, as many of them are still struggling to fill shelves and staff stores.

Grocery chains said they have been overstocking holiday-meal staples like spices and pumpkin-pie mixes, and preparing more cooked dishes. While some consumers have been shopping earlier and buying more food ahead of Thanksgiving, executives said higher demand and supply-chain problems mean that some shoppers might not find the exact size or flavor of every item they want.