I remember checking on this earlier and the fine print said "one offer per client" or something like that. You could take the position, perhaps, that what you're proposing involves different offers. But the bigger issue may be that it's my understanding that you can't have more than one of the same account type (joint brokerage account, for example) under the same registration information.

I've successfully gotten accurate responses from Ameritrade customer service using email, so you might want to ask directly.