It is an often repeated belief that, independent of drugs or some fortunate genetics, it is not possible to simultaneously increase muscle and strength while decreasing caloric intake. And, while this is somewhat true, it is not always true.
And at least, the idea that you can't put on mass while shredding body-fat is certainly not an impossible one. In fact, given the appropriate circumstances, well timed nutrient ingestion relative to workout, and and an extreme, super demanding stimulus (one that instigates a muscle as well as a neurological reaction) the body can go into an alarm response that disrupts the natural homeostasis of the body, reacts to that "threat" as a matter of priority; and continues to shed body fat in the process.
I am not referring to coordinative strength increases, either. It is indeed possible to maintain strength during a cut with a lot more ease. What I'm presenting is that traditional sarcollemic and sarcoplasmic muscle increases are possible.
A lot has to be taken into account here, though. The nature of the muscle work would have to be brief, but extreme. While in a calorie deficit the necessary balance of amino-acids and glycogen must be delivered at a time where those nutrients can not be afforded to be wasted by the body. In states of alarm, the nervous system can fine tune mechanical efficiency resulting in less waste. Lowering body temperature, immediately shuffling proteins to damaged muscle filaments (allowing for a lower percentage of overall degradation in the conversion process), adjusting resting heart rate, and metabolizing fat are some of the ways the body can do this.
There's two sides of this, though. For one the body usually slows down under a calorie deficient condition. With less food and more fat being lost, the body is just as preferential at dispensing with muscle than the rest. Thus is the problem referenced above: the best you can traditionally hope to do while cutting is to maintain strength, and even then you'll likely not come out with any loss of muscle.
However, in accordance with the SAID (specific adaptation to imposed demands) principle, there are a few ways to temporarily short circuit the "starvation" response and go anabolic and catabolic concurrently. The best example of what extreme, brutally intense training can do to a physique is reflecting in a sprinter. Sprinters, actually performing VERY little work relative to their counterpart long distance runners, by and large are: more muscular, carry less body fat, and look denser. World class sprinters do very little long distance running, instead focus on bouts of raw energy, and their adaptive response makes that case for them. I don't want people to lose sight of this in general, either. When you do endurance style activity, your body is not going to prioritize getting rid of fat! It will most likely prioritize shrinking out the muscle! The body recognizes that FAT is what it needs to sustain the lifestyle imposed on it. Contrarily, the larger muscle and the glycogen supplies that accompany them become expendable. All the endurance athletes I worked with, all of them, looked proportionally atrophied and flat. Their conditioning is impeccable because it follows a physiological principle of specificity. You can't optimize two things at once.
What happens then when a sprinter and his fat levels? In accordance with the oft-referenced SAID principle, IT DIMINISHES. To be fast, your limitation is the adipose tissue slowing you down. To be enduring, your limitation is biologically expensive and less conditioned fast-twitch muscle.
And while the sprinters have body fat percentages that are low, long distance runners (despite "burning" far more calories) typically look flabbier, less developed, and are more prone to have distorted posture. Slow-oxidative fibers perform all the action here, and the fast twitchers atrophy. Optimizing one path will, by necessity, diminish the other to some degree.
Example: If you look at the spine, you will notice a variety of compromises engineered for function. Composed of three layers, the hard resisant outer portion is walled with collagen fibers organized together at 30 degree angles. The way they are bound offers imperfect but relatively exceptional protection for compressive and angular force. Inside is predominantly glycosaminoglycan (saccharides). Combining with water, they become semi-viscous and act as an impulse responsive shock absorber. The third portion is involved with the flow of material in and out of the vertebrae. What seems to have been ignored in most of the anatomy classes I've taken is the lower lumbar muscles and the way that they anchor the entire system. The muscles around the hip are always compressing and stretching. If you turn left or right, the torquing movement is absorbed by these muscles and largely responsible for 90 percent of people not having some nerve or spinal cord injury.
Good design is identifying the function, and working to achieve what is necessary in the best way possible! Of course, the backbone could have been HARDER but then we would not be able to move. The bones could have been rubbery but then we wouldn't be able to stand. Essentially, for the function of human beings, the spine stands as a perfect compromise.
Now, proceeding to the point, our bodies operate on similar principles. You can't be OPTIMALLY powerful and OPTIMALLY efficient at the same time. Think about a drag racer. Extra heat, noise, and displacement are examples of energy that is WASTED by the motor as it climbs up the ladder of power-expression. A drag racer can't maintain that intensity for 100 miles. As the motor works at that level, the gas conversion is less efficient, the heat lost eventually warps the internal components, and the louder noise it makes is energy wasted, too. A smaller motor, because of the less demanding nature of its design, eliminates those problems and will be able to do far more WORK (force x displacement) but fall way short of POWER (work / time).
As our bodies engage stimulus, they respond to meet that stimulus as a threat. Physical adaptation is the body adjusting; compromising for a better opportunity to survive. There are very few options for the muscle system when it is stimulated by barbell: increase diameter of the muscle (which usually accompanies a glycogen increase in the sarcoplasm), code for a more efficient movement pattern, do both, or succumb to the exhaustive state. The good news is that even in a caloric deficit, with the right proportions and timing of nutrients, you won't hit that exhaustive state immediately. From my experience the only way to get the optimized response is to impose demands on the body that damn near make you sick.
More on my experience when I was still training, there is a correlation between "shaky" and "uncoordinated" weight training movements and poor neurological adaptation. The story is that at the time, having a very advanced level of muscle, impressing my body to respond and generate already expensive tissue would be difficult. So I picked exercises I had not done in years, exercises that made me look relatively weak, and i worked out with a demanding intensity that took advantage of my neurological unfamiliarity. My own personal belief (and this is case study analysis, not deductive) is that IF a familiar exercise is used by a trainee and he becomes prolific at that exercise, DESPITE the intensity or pushing to muscle failure (or what have you), the net demand experienced by the body will be substantially lower. Even though there is a true MUSCULAR imposition, the nervous system is not in a panicked condition because it demonstrates control over the imposition by being effectively tuned with the motion. However, when a developed muscle is exercised with a movement it is NOT FAMILIAR with, not only is the muscle itself TAXED more (more motor units must be fired to compensate for the lack of precision) but the nervous system itself will arrive in a higher state of alarm. The demands, now increased to a level that is disrupting the entire static environment the body prioritizes most, disrupt the body dramatically. Biologically threatened into heterostasis, the body ALWAYS responds severely. Viruses and bacteria and gun shot wounds are some of the things that disrupt this condition.
And I'm not saying the nervous system does not get taxed enough with traditional weight training, it most certainly does. I'm drawing a point to the NATURE of the demands and what I think is required for someone to achieve it.
Finalizing my story: After two weeks, having doubled the volume, lowering the rest sets, and increasing the tension time (all while maintaining form and gradually increasing weight), I had managed to increase every body measurement except for my waist. Having lost close to a half inch in that time and a belt notch. My calorie deficit was 500 a day, meticulously taken, and the deficit was not modified despite my higher physical energy expenditure. I alertly timed all the glucose and protein supplements i took to correspond with my bodies need for them. Shifting a hungry body into an anabolic condition is about 1)stimulus and 2)macro-nutrient timing. I stopped after the brief two weeks because I'm certain such conditions would have destroyed my health. What made me decide to not continue was a sporadic eye twitch that developed the day after my final workout.
Having put forth my insight on this topic, I am aware that such exhausting procedures can not last long. I would hypothesize that more than 10-20 days featuring more than 7 or 8 workouts would cause a vicious overtrained state. Don't underestimate how stressful exercise is on the body. Maintaining this kind of program, especially on a calorie deficit, will probably make you sick as hell and atrophy your muscle like a penis is cold water. Differing opinions, I'd love to hear!