Almost certainly multiple factories.
These days, it rarely makes sense to do the manufacturing in-house, unless that manufacturing IS your core business. But with Barkbox, I’m guessing they’re more of a intellectual property/marketing type business (i.e. they think up/design cute toys and market them to dog owners). So it makes sense that they’d outsource that to someone else- otherwise they have to deal with all the headaches of sourcing raw materials/components, manufacturing them, warehousing them, etc… None of which is in their dog toy design and marketing wheelhouse. And likely none of which they can do cheaper or better than having someone else do it.
Plus, it gives them a lot of flexibility. If they want to make a solid rubber toy like a “Kong”, they can design it and outsource it to a plastic/rubber casting outfit. If they want to do a stuffed toy, they can have someone do that. Or anything in between. Or even stuff like rawhide chews by some other manufacturer.
Now if your particular business is making say… fish food like @Dallas_Jones describes, then you have some other options. You can do it yourself, if you think you can do it cheaper or better. Or you can contract it out to other producers. Lots of microbreweries do this when they get to a certain size, or if they start marketing it somewhere else. That’s what Samuel Adams did- when they got above a certain size, they contracted other large commercial breweries to brew and package their beer. Kona Brewing in Hawaii did it when they expanded to the mainland- they contracted with Widmer Brothers to produce their beer stateside.
Similar setups abound in the food production business- it’s particularly common in things like condiments (barbecue sauce comes to mind)- someone schemes up a nifty recipe, then contracts with one of these companies to produce X bottles to that recipe.
Basically there’s a lot of specialization in today’s business world. Almost any aspect of a company’s operations can be outsourced in some fashion- payroll, IT, production, etc… The big question is whether it’s cheaper and better to do it that way. The pendulum is starting to swing sideways in IT; some stuff is being brought in-house that used to be outsourced, but other things are being implemented as “Software-as-a-Service”, which is sort of like outsourcing, but sort of not. The in-house/outsource debate is one of those critical business decisions that owners/execs have to make.