Here in NZ (but also in Germany and I'm sure other places) we use MMP - it's pretty simple - take your existing setup and halve the number of representative seats - we all get 2 votes the first vote chooses a local representative for your local seat. The 2nd vote is for a party, each party provides a list of candidates before the election, you count up the parties who have won the local representative seats, then hand out the same number of list seats so that the proportion of seats in total (list and representative district) match the proportions of the party vote - some places have a minimum threshold (3-5%) for a party to be included in that count.
Germany is a little bit more complicated as we also take into account proportionality on the level of each state. And you (at least in general) more than double the size of parliament. But the gist is correct.
