Is that a good idea? I'm not sure, and apparently enough EU states weren't sure that this never got past Council.
But even if it's a great idea and gets implemented it doesn't care about moving money from one account to another itself which is all we're talking about here.
Sales or gift taxes could apply. So could import /export taxes depending on the endpoints. Could it appear as income/gains to one party or another? etc...
of course it can often be structured to avoid such taxes, but it requires forethought.
I wouldn't even think of making a $multi-million move without first consulting a very high end attorney in the appropriate field.
But that is off-topic - the topic is anonymous transfer for unspecified reasons.
Even transferring between two accounts of different businesses you own can generate SARs (Suspicious Activity Reports) at $5K level. Even multiple deposits of a few $thousand in cash will draw attention & be subject to confiscation if you don't have a solid & documented explanation, such as running a big & legitimate cash business.