The goal to make life multiplanetary would be part of more abstract problems - enjoying the exploration of the other worlds, and assuring the continued existence of Earth life.
Currently, Earth life exists on a single planet Earth, and is vulnerable to a number of planetary hypothetical extinction-level events. The probability of an extinction-level event on Earth over the course of a century is estimated to be around 9.5%. It is obvious, that whatever a planetary catastrophe happens to the planet Earth, we would reduce the risk associated with its probability more than 10 times (0.095*0.095 = 0.009025) by having our life on two independent planets, and further reduce it exponentially by inhabiting more planets.
There are very few events, that could simultaneously affect two planets in a single planetary system, among which perhaps only - superintelligence, instability of the Sun, a nearby gamma ray burst, a nearby supernova, a nearby black hole, and some other esoteric ones.
Having independent Earth life on multiple planets would decrease the likelihood of Earth life going extinct from things like an asteroid impact, a supervolcano eruption, a climate change, a global pandemic, and even a low-intelligence nano-bot grey goo.