The practical answer
Humanity has been "genetically manipulating" plants, animals, and to a limited degree, humanity, pretty much since the dawn of time — through breeding. This isn't quite what you mean, but it's a necessary starting point. Humans breed animals for all kinds of reasons.
Charles Darwin may have been the first to describe the process of selective breeding, but the practice may be more than 2,000 years old. The Romans are said to have practiced selective breeding among their livestock, favoring cows that produced a lot of milk. But it wasn't until the 18th century that farmers began practicing it on a large, industrial scale.
Today, farmers breed chickens to have extra-large breasts and to lay a lot of eggs. A wild fowl — a chicken that lives in the woods — lays between 20 and 30 eggs per year. In contrast, a chicken born out of selective breeding can lay as many as 300 eggs per year. (Source)
Which leads us to an important negative:
Temple Grandin, an animal welfare advocate, notes that breeding animals for size
and strength interferes with natural animal processes. Breeding roosters for muscle, for example, can make them top-heavy and unsteady on their feet, interfering with their courtship dances. This, in turn, can alienate them from hens. (Ibid)
so when you ask the question, how strong can they get? That's a very simple question with an incredibly complicated result. Temple Grandin pointed out two consequences. One was an "infrastructure" problem because the Rooster wasn't inherently changed, resulting in a "natural" consequence (top-heavy). But she also pointed out a "behavioral" problem (no hens for you, suckah!)
So, from a practical perspective, if your unspecified condition is "my species must remain, intrinsically, the original species" then the answer is "not a whole lot beyond what body-building can do."
If, on the other hand, you're willing to change your species into something not the original species (because you don't really know what the consequences will be. Your genetically modified species may not even be able to breed with the original stock), then the sky's the limit. After all, you can genetically modify them into dinosaurs.
The literary answer
There are two literary answers.
- Do what you want, don't worry about the science, and have fun.
If you focus too closely on the specifics of science you'll quickly discover (a) that you can't really do what you want to do and (b) that you've dug yourself into a hole that's stopped you from creating a really good story. You'd be surprised how many authors get caught like this. If the purpose of your story is to demonstrate science, then maybe you need the gory details. But most stories are closer to the boy-meets-girl type where the science is uber-cool window dressing for the story you're actually telling. In that case, being too focused can actually distract from the story.
- Use the limitations, as we understand them, to your advantage.
IMO, this is the more entertaining path to take. The truth is, we can't do what you're suggesting. Humanity is just scratching the surface of non-selective-breeding genetic modification. In other words, we don't actually know how to do what you're talking about, so any answer is just supposition.
But, as Temple Grandin points out, we can evaluate the consequences of genetic modification. Increasing muscle strength will only take you so far. Eventually you need to modify how muscles connect to bones, then you need to modify the bones, then you need to modify the nervous and circulatory systems... See the problem? Increased strength means increased metabolism... eventually you need to change almost everything (unless you take path #1 and simply ignore the details).
But those limitations... Author Larry Niven explored them a little bit in his Ringworld stories. The Pak Protectors had enlarged elbow and knee joints to allow for a much larger moment arm (i.e., much more leverage). This increased their strength, but it also mean getting hit by one of them was a honking big deal. It's the difference between being hit by someone's fist and by the end of a golf club (the hands holding the club creating the larger moment arm). But it also made them "a parody of the human form done in cantaloupes and coconuts."
So, I'd recommend you ignore the question of how strong your species can get.1 Make them as strong as you need. But ask yourself, what might be the consequences of that strength? How must the body be changed to achieve my needs? How would that affect this member of my species? Etc.
In short, incorporate the limitations and consequences into your story. IMO, it'll make a far more interesting read than explaining the science behind the genetic engineering that brought the modified species about.
1 Questions like this inevitably fall into a category I describe like this: How much wood would a woodchuck chuck if a woodchuck could chuck wood? He would chuck all the wood that a woodchuck could chuck if a woodchuck could chuck wood. Or, if you prefer, how many angels can dance on the head of a pin? Answer: as many as wanting. See my point? The specifics of the science are irrelevant unless your story absolutely depends on it for a critical plot issue. Just choose how strong you want them to be and move forward.
