I'm going to say 'no' (or at least that you're not going to be very successful), based on my own similar experience.
We use the same sticker arrangement in my state, and I had so many a couple of years ago on my oldest plate (easily 10+ years, probably 15 or more) that I decided to remove the old ones, as I wasn't sure the latest one would stick properly (or someone might take it - see below).
I didn't soak the plate (and I think that's your best option, btw), but rather used a utility blade to remove as many of the old stickers as I could. As you've found out, the adhesive they use on these is very good - and with time, they become very brittle. So they don't tend to be removed easily - or individually. I wasn't trying to do what you want to try, but I know if I had - it would've been very frustrating, to say the least.
In recent years in my state, they also started scoring the sticker diagonally in both directions - so that an attempt at removal tends to get you about 25% of the sticker, if you're lucky - not the whole - no matter how careful you are. This was done to thwart removal attempts by thieves - we had a time where people would steal others' stickers and place on their own. Now they've changed it again, where they removed the scoring, but print the plate # on the sticker itself, to further deter theft. But I digress.
Based on what I saw when I removed my 'stack' a couple of years ago, I think your most likely outcome is that you *might* get down to the original sticker - if you're very, very lucky and careful. And soaking would be your best start to that process. But all or most of the full series, separate and intact - I very much doubt you'll be able to do it. Further complicating things is that your plate appears to be like mine, in that it has a ridge / indented area for the sticker area - so you wouldn't have a flat edge with enough room to get down to the last few stickers, at least in the left and bottom corners.
If you do try it, and manage to have some degree of success, post pics - I'll certainly take a look at your results and give you an 'attaboy' for your hard work (for what that's worth). But I think you'll find it a frustrating exercise - if you go into it with that mindset, you'll minimize disappointment (in inverse proportion to the amount of time you spend trying!)
