In the case of a monopoly on something (railroads aren't really the greatest thing to have a monopoly on, because taking the train has so many substitutes - the ideal would be more like water and air), the number of sources that you wish to own is "all of them." If you lose even one source of that something, that's quite bad, worse than losing the second.
In general, there are two ways of avoiding the un-realism of increasing marginal utility - either have there be some upper limit on the valuable stuff that prevents it from getting out of hand, or have the marginal utility only be increasing within some common domain but decreasing eventually. A monopoly is more like the first of these than the second.
But a monopoly wanting all of something isn't the same as increasing marginal utility, it just means that marginal utility is always positive. For increasing marginal utility it has to be the case that each unit increases the value of the monopoly more than the last unit. Once a network has become large enough, you can ignore the existing network for the purposes of comparing the marginal utility of additional nodes in it. For monopolies that aren't based on network effects but pricing power, you get most of the pricing power at market shares significantly...
Most resources you might think to amass have decreasing marginal utility: for example, a marginal extra $1,000 means much more to you if you have $0 than if you have $100,000. That means you can safely apply the 80-20 rule to most resources: you only need to get some of the resource to get most of the benefits of having it.
At the most recent CFAR workshop, Val dedicated a class to arguing that one resource in particular has increasing marginal utility, namely attention. Initially, efforts to free up your attention have little effect: the difference between juggling 10 things and 9 things is pretty small. But once you've freed up most of your attention, the effect is larger: the difference between juggling 2 things and 1 thing is huge. Val also argued that because of this funny property of attention, most people likely undervalue the value of freeing up attention by orders of magnitude.
During a conversation later in the workshop I suggested another resource that might have increasing marginal utility, namely trust. A society where people abide by contracts 80% of the time is not 80% as good as a society where people abide by contracts 100% of the time; most of the societal value of trust (e.g. decreasing transaction costs) doesn't seem to manifest until people are pretty close to 100% trustworthy. The analogous way to undervalue trust is to argue that e.g. cheating on your spouse is not so bad, because only one person gets hurt. But cheating on spouses in general undermines the trust that spouses should have in each other, and the cumulative impact of even 1% of spouses cheating on the institution of marriage as a whole could be quite negative. (Lots of things about the world make more sense from this perspective: for example, it seems like one of the main practical benefits of religion is that it fosters trust.)
What other resources have increasing marginal utility? How undervalued are they?