For wealth that has already been hidden, it will be hard to tax it. Rather than create a whole bunch of new laws trying to get at it (and which will eventually be applied to the middle class), maybe it would be better to let this wealth release itself into the consumer/philanthropic economy over time. It takes about three generations of heirs to whittle away the vast fortune of their ancestor.
What we should focus on is convincing the wealthy to pay their taxes. Some wealthy people already recognize their wealth is due to the good fortune for living in a civil society. Further education should help convince a few others not to play shell games with their earnings; just pay the tax.
Which brings me to an anecdote with a tax accountant I used to know. He said: "Always pay some tax." I believe he was trying to convince his clients to not get too crazy with tax avoidance schemes for not to raise red flags with tax auditors. Going through an audit is not fun, especially if one has been bending legal and ethical corners.
To minimize tax avoidance schemes, I would recommend that society limits the number of shell companies and/or the shell companies must have a viable business reason for existing. In other words, we make it too easy to create shell companies. If a trail of corporate holdings looks to be mostly for tax avoidance, let's write some laws to get some taxes.
For offshore banking havens, we need to establish a world government of some sort--which is a whole other topic for discussion.
Another tax avoidance scheme that was popular circa 1990 was for Canadian oilfield workers working internationally. They would often set up an offshore company. The company would bill their employer. When the worker returned home, the company would pay him. For example, in 1990, a good Canadian oilfield salary was $50,000, maybe paying 30% in tax. Working international probably doubled or tripled that. But if the worker brought it back to Canada in that same year, he was taxed at 60% . So the offshore company would pay the worker a lower amount, but over several years. The worker legally paid those taxes. And often the offshore account had a credit card where the worker could buy things in Canada, which was, in essence, bringing money into Canada without the tax auditor being able to tax it.
I kind of bring this up because we should ask ourselves: is it really worth it for a society to force this person to pay more tax, especially if the money was earned outside of Canada--and slowly coming into Canada?
When I was an avid reader of THE ECONOMIST, they were big proponents of VAT (consumption) taxes as a means for governments to get revenue. Where this magazine is these days, I cannot say.