First, we present a combined analysis of $pp\to \mu +\nu \mu e-\nu ¯e$ and $pp\to \mu +\nu \mu e-\nu ¯ej$ at next-to-leading order, including both QCD and electroweak corrections. Second, we provide all-order predictions for $pp\to \mu +\nu \mu e-\nu ¯p+\mathrm{jets}$ using merged parton-shower simulations that also include approximate EW effects. A fully inclusive sample for WW production is compared to the fixed-order computations for exclusive zero- and one-jet selections. The various higher-order effects are studied in detail at the level of cross sections and differential distributions for realistic experimental set-ups. Our study confirms that merged predictions are significantly more stable than the fixed-order ones in particular regarding ratios between the two processes.