If the economy is a car then people saving extra is the equivalent of hitting the brake pedal and people spending more is the equivalent of hitting the accelerator (or gas) pedal.
So the huge cash reserves of large companies are a brake on the economy which is why all the politicians are so keen to increase corporation tax /s
I don't really understand how increasing corporate tax could encourage corporate spending. It seems to me the opposite is the obvious mechanism. The more money that goes to the government, the less money a corporation has to put into the economy. If the corporation is in a "save" mode, they're more likely to spend less if they are taxed more than they are to continue the same spending and save less.
Maybe that's not what you're saying or maybe the effect is different than I'd expect (economics is weird sometimes) but I don't get your point there.
Right now companies are saving up profits in their bank balances. I think if you increase the tax they pay then those balances will grow more slowly and the tax money will flow into the economy via the public sector. You think the companies will spend less but I'm not sure why companies would scale back operations?