Pizza dough keeps breaking through plastic

Use a 'big enough' baggie or 'big enough' rigid container. Most dough recipes call for the dough proofs (rising of the dough) to be double in size.

Use a baggie or container 2-1/2 to 3 times the pre-rise size of the dough ball

Many recipes call for an oiled/grease vessel covered with cling film (plastic wrap), kitchen towel or damp kitchen towel to allow for the dough to proof/rise.

I have never encountered a yeast dough recipe or anyone's recommendation to 'wrap it in plastic' film

I'm not going to claim it's foolproof, but there are some possible approaches:

1. Use a recipe that's intended for refrigeration. High hydration doughs in a sufficiently sized container will slump before it gets to the top of the container. Others will specify what size container to use.
2. Reduce how easy it is for the dough to climb up out. A well-oiled dough ball and bowl will have a more difficult time climbing out of the container. You also want to make sure the container is sufficiently large (3 to 4 times the size of the dough ball for typical pizza dough)
3. Restrain the dough from climbing out. A completely sealed container won't work (the lid will pop up after a while), but you can place a plate or loose lid on top of it, then something else heavy on top.

So, my typical technique:

• Put some oil in a container at least 3x the volume of the dough ball, then turn the dough ball over in it 'til it's well coated ... then smear it all over the sizes of the container so both are well coated.
• Press some plastic wrap against the dough ball
• Put a large enough plate on top of it to cover the container
• Put the container in the oven, then something else on top of it to take up the space between the plate and the shelf above (or top of the fridge)

Foolproof way: lightly oil the dough ball and place it in an empty bread bag. Remove all excess air from the bag, then twist the end of the bag closed and tuck it underneath the dough ball as you place it in the fridge.

This has numerous advantages: in a cold ferment (CF) dough, you generally want it to be cooled as quickly as possible. This method maximizes surface area exposed to the cold air without the insulating walls of a plastic container getting in the way. It also removes all excess air space which prevents condensation from happening. Additionally, it allows for expansion to take place (the bag will simply untwist slightly), yet the weight of the dough ball itself assures that it remains sealed.

Avoid using a ziplock bag, as you generally can't remove enough air before sealing it to prevent condensation from occurring.