Speaking about the Roman army, most definitely. The Roman soldier was able to carry a week's supplies when necessary.

There were multiple types of trains, the troop of mules integral to the Imperial legion (one mule per contubernium), the army train with equipment and provisions for the entire force, the officer's train with their personal equipment, and a siege train.

This is separate from supply trains that would operate between the port and supply bases along the route of march.

With each soldier requiring (roughly) 1.2kg of food each day, then the 8-10kg of hard and dry/green fodder for horses and mules, the amount of food you need each day quickly adds up into the tons. To move all that you'll need wagons and the oxen pulling those wagons are going to need to be fed - cutting into the amount carried. Past 10 days of marching you hit diminishing returns on food carried versus food consumed by your transport.

The Roman ability to feed their army in the field year round is an oft-neglected reason they were so successful.