Is it possible even in principle to calculate things like CPI-U from publicly available raw data? It would be really cool to have access to time series prices f

Is it possible even in principle to calculate things like CPI-U from publicly available raw data? It would be really cool to have access to time series prices for broad swathes of goods amd from various locations across the country/world. I'd be interested in playing with that data to see if the official numbers are reproducible. Also, it'd be cool to see how well one could predict future prices of certain goods, like toilet paper. We probably also want data on the spending habits of various locations and demographics.