Two days between Paris and London

I would just add your days to Paris and London, and do a day trip from either or both. In fact, with only four days in London (especially if that includes any travel days) I wouldn't even do a day trip from London, as there is so much to see. If you are going city center to city center, I would take the Eurostar. Book as soon as you know your travel dates, and dates are released, for the least expensive prices. For more on the Eurostar, see The Man in Seat 61's website.

The reason I wouldn't add a third location is that it is more time and money, to change locations, when you would only have one night in a third location anyway, so you can pretty much achieve the same effect by just doing a day trip and save the hassle of packing and moving.

But it's your trip, so you should do what suits you. Hope you are able to come up with a plan you enjoy.

I agree with Kyra. There are dozens of great day trips from Paris. Here are a few:
https://janettravels.wordpress.com/category/day-trips-from-paris/
And in addition there is Chartres, Verailles, Giverny, Rouen, Auvers sur Oise (where VAn Gogh lived his last days and full of sites he painted) and many many more. From London you could do Canterbury or take a day trip out to Stonehenge and the nearby Cathedral or even do an overnight in Bath (I did this years ago when my daughter was 12 and we had a wonderful time including afternoon tea at the Pump Room where Jane Austen's characters enjoyed it).

Another possibility is to do a night or two in the Loire and visit chateaux -- but you want to be in Paris to get the Eurostar and so a side trip overnight between Paris and London would make travel awkward.

I agree with Kyra. By far the most efficient way to get between Paris and London is the Eurostar train. It makes very few stops between those cities -- only Lille I think, and getting off there and on later will probably add cost, and Lille wouldn't be on many people's lists of best stopovers.

A simpler, more convenient strategy would be more nights in either Paris or London or both, with a couple of day trips. There are many threads on the France and England boards about good day trips from these cities. My two cents would include:

From London: Oxford or Cambridge, Canterbury, Salisbury and Stonehenge, Bath, Brighton, Portsmouth, even York if a two-hour train ride each way doesn't faze you. Not to mention closer-in Windsor, Hampton Court, Kew Gardens, Greenwich.

From Paris: Chartres, Reims, Rouen, Giverny, Fontainebleau, or closer-in Versailles or St-Denis.

A couple of extra days is a good problem to have. Enjoy solving it! ;-)