cities-skylines
A lot of my office zones seems to be on the cusp of reaching the third level, but it would never reach it. I placed fire stations, police stations, parks, and just about anything I could think of that an office would need. I also have a surplus of highly educated citizens, so that doesn't seem to be the problem.
What are the requirements for office zones to reach their max level?
I haven't found any (official) evidence to prove my hypothesis following now, so be aware that it might be wrong.
You say that you have no industrial zones at all. So, let's check this chart first:
You see that there's a production chain which requires specialized and generic industry to create goods for your commercial buildings. If you had that, you could easily lower the import rate. However, you don't have those buildings or zones so basically you import everything. You can read here too that offices are a clean alternative to industry, nevertheless they don't produce any goods.
I guess the whole problem is that you miss industrial areas. Your problem isn't well documented nor reported because it doesn't occur that often. Most cities have industrial areas, you and few others don't have them and are suddenly facing the problems of too less goods. As you can also see here, offices have some downsides:
As a fellow city builder, I can just recommend you to build up some industry. The flow will be way better and less troublesome. Yes, you have pollution. Just be a dirty (real life) mayor and hide anything negative from your citizens by placing it far away from them and covering it up.
As said in the beginning, I don't have any official evidence supporting my hypothesis, but I hope I could still help you with it.
As Dennis noted, service is a huge part of this - all the services in the game only work if transportation is available (of course, power uses power lines, water uses water pipes, so they aren't affected by road traffic).
This gets worse as the city grows bigger - it's very easy to have all your service trucks stuck in one traffic jam. Note that the service buildings don't have a finite range, the way it's indicated in the UI - that's just the range where they're effective. They will happily travel through the whole city, through three different traffic jams to get to a point where they are needed, and then back again. There is a limit to how long they can spend on a trip, but it's pretty long. Something that looks like a fun traffic jam in a 20k city will completely paralyze a 60k city. Seriously, I've had a city drop from 80k to 50k over a few weeks, just because of traffic jams!
Industry can only work if it has the resources. If you're seeing many abandoned buildings, this is one likely cause. This is much more important when you have e.g. wood industry without a forest - all the wood has to be imported. Industry creates huge traffic in the mid-late game.
And I've observed increased taxes after fixing traffic issues. I'm not sure about the cause, it might be that commercial zones produce more money when they get people-traffic. Or it might be the better service access, who knows.
And of course, traffic jams add a lot to noise. This can be countered (trees), but it's a factor.
Best Answer
Along with the "big" city services like education and fire, there are a few other things to check and to provide if you want your buildings to upgrade.
The first that I would suggest you look at is public transit. Any kind will do, buses, subways, trains, whatever.
The next thing to look at is your data overlays. What's the pollution like in the area? Noise? Upgrading the nearby streets to be tree-lined improves noise pollution and can make people happy.
As a general principle, anything that makes those little smiley faces pop up over the buildings is increasing their happiness and moving them towards upgrading.
Note that these work for any kind of building that can upgrade, including industry. Non-office industry once upgraded produces less pollution and employs higher educated citizens. Just noting this because its something that I see a lot of people neglect (Parks? In my industrial area?!).