Remember, when you are cutting, you aren't looking for gains so much as you are looking to maintain what you have, so doing more work isn't a problem as long as you can handle it. I find people often need to keep calories at maintenance when they do 6 times a week, however, or they can't handle all the extra work. Obviously all that extra work creates a large calorie deficit... and since it is better to create a calorie deficit through work rather than diet, it can help you spare more lean mass than you would otherwise.
Of course if you can make strength gains at the same time, then that is great. But like Fausto said, it takes some planning. You don't want a big workout. I would stick to four to six lifts and only do one or two sets for each. The extra frequency will make up for the low volume.
For an even bigger boost, you can try an AM/PM split, done six or seven days a week. With that, you would want probably four lifts, one set each for each workout, possibly alternating exercises as well.