Is there any way of having a SketchUp 2018 license installed but also having the option to work in 2016 as most people in our office use 2016?
You should contact Customer Support directly about this but normally no. You can save files back to SketchUp 2016 and of course open files made in SketchUp 2016 with SketchUp 2018.
It is entirely possible (and common among extension developers) to have more than one version of SketchUp installed at the same time on a single computer. They co-exist peacefully, the only issue being keeping track of which version created each file you work with.
However, a SketchUp license is version-specific. You can not run SU 2016 using your SU 2018 license or vice versa. If your office has a network license, you should be able to get 2016 and use that license. If not, as @DaveR said, you will need to contact customer support to see whether they can help.