If you looking at a technologically advanced species, one thing you need to consider is the significant difference between the physical evolution and the technological evolution. The differences between these makes it possible that two sapient species could evolve at the same time.
As a species, Homo sapiens came into being 200-500 thousand years ago. This means that if you had a time machine and brought a young child from then to our time, they would be able to fit into modern society1.
We know that agriculture has been around for at least 10 thousand years. So it took over 90% of our existence as a species so far in order to develop agriculture. Agriculture has allowed us to live in much larger groups. Living in large groups, we have the ability to systematically destroy any threat that consists of only small groups. This is why reaching the milestone of agriculture means dominance over non-agricultural threats.
So now, what about that window of 190 thousand years? What if another species capable of developing technology evolved during that period? It would be a race to develop agriculture, with the winner being the species that developed it first. This means that it is very unlikely that there could be multiple dominant species unless the two species did not have to compete with each other.
Consider the dog. According to the first result of a quick Google search, there are around half a billion dogs in the world. Most people would agree that they are not dominant, but dogs are clearly doing well as a species without any level of technology at all. They were able to attain this status by being capable of things that we can't do and helping us.
Over time, dogs have been bred to emphasize the traits that we find useful. One result of this is that most dogs have been bred to be more obedient. As such, dogs have proliferated by not even trying to be the dominant species anymore.
So what needs to happen to have multiple dominant species? They can't be in competition, or else the first to agriculture will likely wipe out the other. Also, they should be of roughly the same level of intelligence, with other features to distinguish between them. For example, suppose one species is stronger and the other is quicker. This would allow for interesting ways that the two species could work together—predators against which the stronger species has a distinct advantage, and others against which the quicker species has the advantage.
Another possibility is, as others have mentioned, physical separation. Suppose that instead of being different races, Africans and Europeans had been separate species. By the time of the "Age of Discovery", European society had advanced enough to no longer be immediately concerned about survival. The Europeans would likely have still chosen the slave trade over extermination. The slave trade may have lasted longer with the Africans being a different species, but as society continued to progress it would still be eliminated. It still would not have been enough time for intelligence to be bred out of the African species, allowing them to join the European species as dominant.
1. Assuming that the child did not have mental disability due to malnutrition during their mother's pregnancy, diseases that we no longer have to worry about, etc.