Take the German system: there are district level elections, so that there is one person elected in each electoral district. These get half the nominal seats. Then the other half of parliament is filled up with candidates to match the proportional vote. The fill up is a bit complicated, especially if a party has a lot more directly elected folks than proportionally mandated, which leads to growth of parliament and discussions how that growth can be avoided. (Larger districts and only 1/3 directly elected or not every directly elected candidate really making it or not holding up the exact proportionality or whatever) But it combines the factors mostly fine and avoids many of the problems of the pure systems.
If you elect, oh, 5 people in each district then your proportionality is still granular to about 17% of the vote in the district (for single member districts it's granular to about 50%, of course). And your districts are 5x as large as single member districts are for the same number of representatives. What it does give you though is better electability for local independents.
With mixed-member proportional you can easily get down to couple-percent granularity while maintaining medium-size districts (typically twice as large as single-member).