There are ways that Canada could curb corporations from using tax havens to avoid paying their fair share of taxes. The Japanese government has shown us one way to do this.
Japan has a law called the Tax Haven Counter Measure Law. It applies to any Japanese subsidiary in a low tax jurisdiction with a tax rate of 20% or less. Under this law, the Japanese parent is taxed on the undistributed earnings of these foreign subsidiaries.
In this way, Japanese companies cannot set up subsidiary companies to hold copyrights, patents, leases, etc, in tax haven countries that then lease these back to the parant company for a fee and thereby lower their taxable profits in Japan.
Japan also has the concept of "Economic Logic" which is often used to deny special treatment to companies in tax havens. Under this concept, if the businesses could reasonably be carried on in Japan, the 'economic logic' of them being offshore is lacking, and is hence denied.
There are a few exceptions made. For example, where the subsidiary is in a country where the tax rate is more than 20%, the earnings can be excluded from current taxation only if (i) the company has staff, assets, and premises to conduct the business, (ii) the management, control, and governance is carried out in that country, and (iii) the transactions with related parties are less than 50% of all transactions. This approach effectively prohibits shell companies while allowing corporations to still set up legitimate businesses even in countries with lower corporate tax rates.
Japanese multinational corporations are prevented quite effectively from the use of tax havens by having a very simple law which was first enacted in the late 70's. Yet Japanese companies are able to compete globally. China treats its multinational corporations in a similar way.
The Japanese corporate tax rate is in the range of 38-39%, much higher than the US, UK, and most other OECD countries. The temptation to avoid paying this rate of taxes would be very strong for Japanese corporations and without such a law Japan would probably have a lot of difficulty collecting what was rightfully due.
Although the combined federal and provincial corporate tax rate in Canada is quite low at roughly 25%, many Canadian companies are using tax havens to lower their Canadian taxes.
Some of the most common strategies are setting up subsiduaries in tax havens and then selling their patents, trade marks or other intellectual property to them. The subsidiary then turns around and leases these back to the parent company for a substatial fee. The fee payments become an expense for the parent company, which lowers their profits in Canada, and also the taxes due on those profits.
Loans between parent and tax havens based subsidiary are another way to play this game. Transfer pricing, where a commodity or good is sold to a tax haven based subsidiary which then sells it to a final customer at a much higher price is another commonly used strategy to reduce profits and taxes payed in Canada.
Canadian tax law tries to limit some of these practices by inisting that the "arm's length" principle should apply to transactions between related parties and that prices chared should be in line with what migth be charged if the contracting parties were independent. In practice, this arm's length principle has been very difficult to enforce. It works for commodities such as copper or wheat that are widely traded on open markets, but has not worked very well when it is difficult to determine a fair price such as for drug patents or trademarks.
Japan has shown that there are better ways to effectively limit corporate tax avoidance using tax havens. What is lacking is the political will to stand up to corporate tax abuse.