We may ponder about some good naming for an EIP that remembers an Exchange and then allow to restore that Exchange at a later point.
We could have push/pop as a stack fashion. Or use some kind of naming, push(foo) and then pop(foo). Or some better naming.
People today have stored the message body as an exchange body and then restored that later. But this may be simpler.
For pop we could allow an optional aggregation strategy so people can merge the current exchange with the pop in any way they want.