The answer to your question is "yes we can" develop or conceive of universes with completely separate laws. However, any such speculations are limited in our understanding of how the fine details would work out.
Just look at how bad we are, generally, of understanding even the effects of our own universe most of the time without oodles of data and years, if not generations, of research. For example, look at the historical question of what would happen to man in zero-gravity and space. The vast majority of scientists (who were not science-fiction writers, anyway) believed that man could not survive space. These were the top scientific minds of the time. We had to actually experience it and get some data before we were able to fine-tune our understanding of all the effects.
Some possible examples of alternate universes
Consider all the science-fiction and fantasy literature that's been written. There must be hundreds, if not thousands, of alternate and parallel universes that have been imagined by humankind and recorded in one adventure story or another. Now, granted, the vast majority of those are a 'subtle variation' on our existing universe - typically with some kind of magic possible, different kind of intelligent lifeforms (think Middle-earth, Star Trek, etc.). But I have run across some truly unique ideas of alternate realities - for example the fractal universe created by Piers Anthony (the book is Fractal Mode). While life is roughly the same, the entire geometry of the universe is based on fractals rather than normal 3-d geometry.
I believe that the most unique alternate realties are based on mathematical discoveries. For example, non-euclidean geometry was completely developed prior to understanding that it is, indeed applicable to our world (it can be used to determine the shortest flight on a globe rather than on a flat surface, as an example). The point is not that it ended up being an alternate universe, but it was a set of rules that we were able to develop without any understanding of how it applied to our known reality. Mathematical reasoning and logic can allow us a starting point of being able to prove or disprove how things might work under an alternate set of laws without having to experience it first.
Another example would be the many different multiverse theories that have arisen from mathematical modeling. For example, take string theory - it may or may not exist in reality, but we can explore what the extra 6 or 7 dimensions are without having to empirically test or understand them through using a purely mathematical/logical approach.
And I actually like the example from Bulat's answer - the worlds that can be (and, in fact, are) created within a PC - not virtual reality worlds, per se, which just model our universe, but at world of information with no true 3-D space - perhaps with time though. Other dimensions are certainly present if you devel into it, and life is certainly conceivable (if not already proven to be possible) within that realm.
I think the core of your question though is whether we can ever have a true understanding of how such a theoretical universe would truly operate. My answer would be mostly no. We would primarily just be guessing and many guesses would be miles off the mark if history is any guide.
Could we have true insights about some of them, some of the time - sure! But just as we can interpolate data much more accurately than extrapolate data - when we have a completely new theory there are often huge disagreements on the real ramifications because we don't even have enough data to even extrapolate! So in that sense, I would say you are partially correct - with no experimental basis to gather any kind of empirical data on a newly conceived universe, we might guess correctly in some aspects how it works, but we could never know for sure. We might be able to simulate some of them - but then simulations always are only as good as their base assumptions and rules for building the simulation.
I would say that as our computational capabilities expand through technology, we gain more and more ability to simulate complex multi-variate systems, and that can only increase our ability to truly "create" such alternate universes, at least in a small-scale, model form. This may give us some basis for real experimentation/investigation into some such alternate realities. This is especially true if they arise from purely mathematical constructs.