But will all of those variants still be considered the "same" sentence? I'm asking because it's popular to make the same claim about Hungarian, but it's not really true. You can switch things around a lot and still get fully grammatical sentences that all relate to the same event. But due to Hungarian's topic/focus structure, the actual meanings expressed by the variants are so different that Hungarian speakers wouldn't consider them "the same sentence expressed a bit differently". Some examples: https://en.wikipedia.org/wiki/Hungarian_grammar#Emphasis
In contrast, I believe Latin is really liberal in its sentence structure, especially in poetry.