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Multi-company structure

In your case, you might benefit from setting up a holding company which owns the local and the offshore company, making the two operating companies sister companies.

However, it depends on where you live and what the applicable laws say. Having a holding company is almost always a good idea, though, as it can offer tax advantages, tax deferrals and other benefits. But it's best to discuss with with a local tax advisor. For example, one complication to consider is how the holding company would take over the offshore company. Different laws in different places say different things about how that can/must be done.
 
What is your intent with this corporate structure? What are you trying to solve? Tax planning? Future handover to your children? Big bang exit in x years? Maximizing investment funds? Or a mix of these? Etc...
Once you know that, it will make it easier to decide how to setup the structure. Just don't overcomplicate it and be aware of the costs, especially oversees "specialists"/tax laywers...most of the time it's a numbers game.