Officially, Easyjet only allow ONE item of cabin baggage,
plus (a) one of the following: An overcoat; an umbrella, or a shawl;
and (b) one standard size carrier bag of goods purchased from the departure airport.

so the answer would appear to be no.

However they may turn a blind eye to your laptop case on the day, or they may make you gate check one of your bags and charge you a fee.

You can't check in your normal carry on without paying an extra fee, but it costs less if you pay this in advance rather than at the airport on the day.