I'm probably missing something obvious, but it won't be the first time
I've been using TransferWise (TW) to send money from our UK NatWest account to Greece. In the near future when (if? *sob*) our house sells I'll be sending it the other way, so thought I'd experiment with a small amount Greece -> UK. The TW account, though, seems devoted to the NatWest account and assumes the transfer is coming from there.
Easy - create a second account with a different email, yes? This fails when the TW system notices the same name, d.o.b. and address as the first account. I've enquired at TW but they're slow to respond.
There must be a way to switch source bank accounts that I'm missing.