While many "contacts" are two hams talking to each other, there are also larger groups, with 5-20 people all on the frequency communicating within the group rather than just pairs of people.
In other words, we multiplex not just frequencies but time on the same frequency as well.
Additionally, commercial VHF/UHF bands have already reduced channel bandwidth and spacing by half to fit in double the channels, and in many areas, amateur radio has not adopted similar measures. So if we were running out of space, there is already 20 year old technology that would allow us to similarly double the channels.
And, as already pointed out in the other answer, within the amateur community itself, we have already developed multiple methods that use a fraction of the bandwidth of existing commercial methods. FT8, PSK31, JS8call are only a few of the digital modes. We also have developed codec2 for voice communication which uses almost half the bandwidth of SSB, and this is 1/5 the bandwidth of what commercial radios use now.