Integrating multiple systems with overlapping but different domain models

I'm writing an integration between my company's inventory management and point of sale software (it's a web application), and an eCommerce platform. The challenge is that both our application and the eCommerce platform take responsibility for many of the same things: customer relationships, inventory management, order creation, fulfillment, and payment, etc. The effect of this is that there's really no way to demarcate responsibility between the systems. I can't figure out how to avoid linking together all relevant functionality between the two systems, i.e., not just processing sales in both places, but managing and delegating voids/refunds, etc., feature-for-feature. The problem is that this really increases the surface area of the integration, and the resulting amount of work required to build and maintain my software.

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Does anyone have advice on how to decouple the two applications, sharing responsibility in the right places and delegating in others?