Assuming that the dimmer isn't actually controlling the load (obviously, in that case you're at the mercy of what load it's actually controlling...), then this is an example of how you can do what you want with Rule Machine: [How to] recreate Philips Hue Dimmer Switch functionality with RuleMachine. You're basically emulating the behavior of the Hue Dimmer when paired to Hue, where repeated pushes of the top button can cycle through up to 5 scenes. In this rule, they did indeed use a local variable to track how many times the button has been pushed (for the Inovelli with the stock driver, this would indeed be "Button 1 pushed" as in the example; most of their other button event choices are...interesting). I do see that rule lacks the "reset" timer that the Hue dimmer has, but you could solve that by adding a few actions to the end of the rule (Cancel Delayed Actions, a cancelable 15-second delay, and then setting the variable to 0, for example).
I also wrote Dimmer Button Controller to make something like the above a bit easier, but it's intended to work with the same set of lights for each push. It would be usable here since a level of "0" means that light will turn or stay off and no level specified will either turn the light on or leave it at its current settings, but I guess its usability here might depend on what you want to happen as you cycle through. (It also gets confusing for button devices that do natively support multiple taps for one button, as it's written to "fake it" on ones that don't, which does not include the Inovelli. It will certainly work if you are aware of that. I'm not exactly sure why you don't want to use those capabilities instead, but I'm not here to ask questions. 
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