Thank you for explaining. She is trying to get out!
It is so difficult as hamster care and knowledge has progressed so much - through research and experiences. I know at one time - maybe 7 or 8 years ago, a 4 level Imac fantasy was seen as a good option for a Syrian.
Ok so she is a female Syrian and they often need a lot of floor space. The theory is that one larger cage, with unbroken floorspace, provides them with normal behaviours and they get less stressed. If she doesn't have a wheel then she probably will go a bit stir crazy. Again some years ago there used to be debate as to whether or not a wheel was necessary but that was concluded and it's well accepted that all hamsters need a wheel! But not a ball
Cages are expensive as well. I had exactly the same issue with our first Syrian! I bought a 3/4 tier rotostak unit - because I'd had a hamster in one before 25 years earlier. I did see stuff online about minimum 60 x 40 (at the time!) and decided the levels would add up to more than that. I had very similar issues to you. The hamster would chew at the only barred area, desperate to get out. He did actually get cage rage as well.
If you have recently bought the Imac fantasy levels that will have worked out quite expensive. I also had that - having spent a fortune on rotostak bits and bobs and extras I then needed to fork out for a new cage - at the time it was an 80 x 50 cage - and the change in the hamster was amazing - he was happy and enjoyed his cage and no stress behaviours. Even then I found I it wasn't quite enough and ended up upgrading to a 100cm cage. So our first hamster cost me a fortune! And had two big cage changes.
I'm not sure where you are - US or UK or elsewhere? I'm guessing US because I don;'t think the Imac Fantasy is available any more in the Uk. I know most people in the Us end up getting tanks or tank style cages because there aren't really any barred cages big enough. There are a couple but they're only minimum recommended size and not a massive upgrade. On the other hand tanks and tank style cages can be big and cumbersome to move around. A detolf is a popular option as well - it's still a tank but also a bit of a room feature as well (especially when on top of kallax units for storage).
As elusive mentioned as well, Syrians need an 11" diameter wheel. I am not entirely sure but I think one of those fits in an Imac Fantasy, but would probably take up most of one unit. Any wheel needs to have a solid running surface (not mesh) for safety. The 12" silent runner is a popular one (from exotic nutrition) but I don't think it will fit as its' 12" (35cm tall on its stand). Niteangel make some good wheels as well but they're not cheap.
I would start by getting a wheel though, making sure it will fit and then look at upgrade options for the cage. Rule of thumb is - add on units are fine as long as one of the cages is at least 80cm by 50cm and ideally 100cm by 50cm.
I think the cheapest option is something like a 40 gallon breeder tank. Apparently petco sometimes have dollar per gallon sales. Or possibly a second hand Exo Terra Terrarium (90 x 45 x 45). Niteangel make a great cage but it costs a huge amount of money. Some people make bin cages but it can be hard to find big enough bins.