Yes, and it’s surprisingly simple: chuck the baby and keep the bathwater. Dan Benmergui’s Storyteller is a flash game in which you don’t play as any particular character. You instead control three separate characters in a three part story-panel. Depending on where you position the characters in the initial ‘Once upon a time’ panel will affect their presentation in the middle ‘When they grew up panel’. Put the girl on the poor, deserted half of the panel and she becomes an evil wizard. Leave one of the men on the green, white castle portion and they become an armored knight. The middle panel features a similar set of options: place the man inside the cage as the prisoner, make the woman the knight, and then dictate the outcome of her duel with the wizard (whom you created). You can use this character placement to dictate how the romantic relationships turn out in the final panel along with who dies and who wins the battle.
This engagement method is, like The Sims, founded along the principles of giving the player a dollhouse to play in. When you add a narrative though, a distinct shift occurs: I’m not guiding the characters to see what happens to them in the plot, I’m directing them to the outcome I've created for them. Frankly, given the amount of time I spent exploring and tweaking three little people and seeing the results, I’d say it solves the engagement problem quite nicely. You can find more of Benmergui’s stuff here.