I daresay anything is possible but it's hurting my head working out how we'd account for any improvements we make to the property.
Short answer, you can't.
There are too many variables in property and the market and you will never know what a property "could have gone for".
Say for argument's sake the only improvement you make is revamping a bathroom, ripping out a suite that didn't prevent you from buying the property in the first place and spending 5 grand to replace it.
By the time you come to sell if the market has grown then you would expect your property to be worth more than you paid regardless of the cost of the new bathroom. But is it that simple? Has "overpaying" in your eyes (you will never know if you actually have overpaid, property is only worth what someone is prepared to pay for it) impacted on your profit?
If the market grows but the property only sells for what you paid plus 5 grand do you assume that you overpaid in the first instance, that the property has finally caught up with the market and that the bathroom added 5 grand of value?
If the market drops and you've invested money to make improvements but the property is valued at less than you've paid overall and you absolutely need to sell for some hypothetical reason how can you possibly calculate what relative value the improvements added in order to work out how much you overpaid by?
That's just a "simple" example with fixtures and fittings. If you make any bigger changes like carving out a new bedroom or removing one that could have an even bigger impact on the property's value and complicate your dynamic even further.
I think this whole thing is a recipe for disaster. You need to agree between you a price you're both happy to pay for the property in the first place.