Has any daycare agreed to keep spare clothes on site?

Twice this month our son has come home in the daycare's emergency clothes because his bag had no spare set. He's 2 and still has the odd accident at nap time, so it does matter. At home the spares get washed with everything else and go straight into his cupboard. My partner and I pack the bag on different days and neither of us remembers to check. I'm thinking of skipping the home system altogether. Send three labelled sets in one go, ask the daycare to keep them in his cubby, and we only replace whatever comes home in the wet bag. Has anyone's centre agreed to something like this? Or do they usually say no because there's no space?