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Installation of heat / cooling transfer system

We have a new build two story townhouse which has a heat pump downstairs but nothing upstairs (where the 3 bedrooms are). The temperature upstairs in winter hasn't been so much of an issue however it got very hot upstairs in summer and we'd like to investigate some sort of transfer system that could take cool air from downstairs and transfer it upstairs. I'm not sure how much ceiling space there is upstairs however there is existing venting between the laundry (downstairs) and bathrooms (upstairs) by way of an in built extractor fan system. We'd prefer to avoid an additional heat pump upstairs as there isn't really any wall space to put it on and we'd need an additional exterior unit