Habitable zones are regions around stars where large bodies of liquid water can be sustained on a planet or satellite. As many stars form in binary systems with non-zero eccentricity, the habitable zones around the component stars of the binary can overlap and be enlarged when the two stars are at periastron (and less often when the stars are at apastron). We perform N-body simulations of the evolution of dense star-forming regions and show that binary systems where the component stars originally have distinct habitable zones can undergo interactions that push the stars closer together, causing the habitable zones to merge and become enlarged. Occasionally, overlapping habitable zones can occur if the component stars move further apart, but the binary becomes more eccentric. Enlargement of habitable zones happens to 1-2 binaries from an average initial total of 352 in each simulated star-forming region, and demonstrates that dense star-forming regions are not always hostile environments for planet formation and evolution.