After some research, I don't grasp how Can the Ebola, Measles, Coronaviruses somehow lead to a new deadlier virus? can be opinion-based. I didn't know it when I wrote the question, but it involves Genetic Recombination, so a layperson would have reasonable cause to ask my question.
One specific type of mutation that a virus can undergo is called "genetic recombination." Since viruses rely on human (or other organism) cells in order to produce their genetic material, if two viruses infect the same cell at the same time, this genetic material is in close contact, and can "cross-over." A layperson has reasonable probable cause to think that
Viruses don't generally have any way to exchange genetic material with each other, no, except in very specific cases like Mimivirus, which can only infect its host if that host has first been infected by another virus named Sputnik, and there's evidence of gene transfer between those viruses.
At minimum, future readers would benefit from knowing the answer that someone adduced by Julia Oh B.A. in biology from Harvard University and her Ph.D. in genetics at Stanford University, rather than seeing my question closed without none.
The virus that caused the Spanish flu didn't exist before 1918. Experts think that it was a mix of human and bird flu viruses.
Most likely someone was infected by both a bird and a human flu virus. The bird flu probably picked up some parts from the human virus that made it easier to spread and harder for the body to fight off.
But, this kind of thing can't happen with the cold virus and Ebola. To be able to do this kind of mixing and matching, the viruses need to have very similar genetic material. And the cold virus and Ebola do not.