I don't think it is possible, unless "nuclear hyper ancient magic, something".
A ten-to-twenty-fold increase may seem counter-intuitive to start with, but that's actually within the realm of "possible". You can get that on normal people with electro-stimulation, so why not naturally on some presumed mutant, if you are willing to handwave a tiny little bit. But the problems are of different nature.
First, while increasing strength (muscular "power") is possible without increasing mass, and while increasing strength endurance alone is possible without increasing mass, increasing both at the same time is impossible (without increasing mass). Your mutants are to lift 20 times as much, and carry that around, so they need both.
Increasing actual muscular power (just to be nit-picky on wording) would require a combination of things, including a fundamental change to your cardiovascular system. Power is energy-per-time, and 90% of your energy comes from the electron transport chain in your mitochondria. Which requires, well... oxygen, and not precisely small amounts. So you need huge quantities of blood flowing through your muscles to supply that oxygen, which is already a practical problem on a contracted muscle of "normal" strength. Now, multiply strength by 20, and you multiply the supply problem by 20, too... Unless you are happy with 5-10 second feats (question explicitly says different), you're kinda lost.
You can activate more muscle fibers at the same time, that's what people who do strength training learn to do at will. It's what most animals (including e.g. apes) do, too. Animals are not magical in any way, they're just not as much of a wuss as the average human because in the real world in which they live, being a wuss means being dead and eaten.
It's more neurological than actually "muscle". Also note that the guy holding the world record in bench press is not necessarily the strongest guy, either. Or the biggest, for that matter. Some stunningly strong people are surprisingly small and slim. Think e.g. Chinese acrobats. The thing is, the more fibers you activate at one time (for more strength), the more fibers get tired (pretty obvious). Which means unless you have more of them, you necessarily have to drastically reduce time.
Second, assuming you can actually increase muscular strength to that level, it would almost certainly mean that your tendons would rupture. Tendons, vaginae, and hypomochlia have to endure surprising amounts of force even for trivial tasks. In hand surgery, one is often surprised why they make such a darn fuzz about holding fingers in some particular position with rubber bands for ages after suturing. Well, the reason is that merely moving a finger will put the equivalent of around 20 kilograms on that little tendon, which is non-trivial for a healthy tendon already, but definitively is more than the suture will support. So imagine what forces are at work when you actually grab something firmly. The force that acts on the various fibrous rings that keep tendons in place and allow them to force the attached bone in some particular predetermined direction can be 10-20 times as much. The forces on your knees or elbows when the joint is in a widely-flexed position? The knee at least has the patella, which somewhat redirects force in a sensible direction. The elbow doesn't. Don't even want to think about how much force acts on that tendon.
Although we're looking at some of the strongest tissues nature is able to build, in reality it often comes close to what the tissue is able to physically support. That's why repetitive strain wears stuff down so surprisingly fast, and it's why there's not rarely... BANG... catastrophic failure.´.
So, well, OK, they're mutants, let's assume they have some magical carbon-nanotube tendons, whatever, which magically support 3-5 times as much. But we talk about multiplying with 20, and not just for a second or two, but supporting that for a lengthy time, I cannot imagine it could work.
Third, there's levers at work. For example, your spine is one huge lever (about a meter long) connected to some small levers (about a centimeter or two). Plus, spinal discs, which are surrounded by a fibrous ring. The disc itself is pretty much indestructible as long as it's held together, but the ring isn't...
The actual force depends on where you look at, but let's just assume there's a ten-fold increase (which is very optimistic). Lift 50 kilograms, so you effectively have 500 kilograms acting on your little piece of bone or your fibrous ring, there. Now you want to lift 6,000 kilograms... good luck. A small piece of innocent bone less than a centimeter thick just cannot support 60 tons sheer. I am not sure if a piece of solid steel would, even. Similar is true for virtually every bone, to a different, individual extent.
Note how e.g. when people die from tetanus or are exposed to electricity, muscles often do break bones. This is not just an idea, it actually happens.