This is more so theory than plans, and this is the only stack exchange that talks about corporate structure
Is it possible to make a new shareholder class, arbitrarily, solely for the distribution of a high dividend?
I was thinking, lets say that a private corporation (or even public, the only repercussion being the media) wanted to give one person a lot of money, could they make a small new shareholder class - that one person buys all of those shares - and then issue a 1000% dividend even several times?
What prevents arbitrary classes of shares from being created, anything?
It is in fact something done pretty often with startups, where early investors want the priority in dividends' payouts.
Depending on the jurisdiction there may be various limitations. In the US, for example, multiple classes of shares can only exist in a C corporation. In many jurisdictions there are laws protecting minority shareholders in cases of majority stake-holder abuse (which what you describe might be treated as), etc.
Bottom line is that technically there's a possibility, but you need to look really well at the local laws as to whether or not it is in fact doable in your particular case, and on what terms and under what conditions.
So (i) doing what you suggest would require amending the corporate charter, and that would need the approval of the other stockholders, and (ii) you haven't mentioned why the company would want to do this -- depending on the reason, the other stockholders may have a lawsuit for waste/breach of fiduciary duty/etc...
However, if a company's officers really wanted to transfer all of the company's cash to somebody else, there are much easier ways of doing it. Just declare him an employee and pay him a really big signing bonus, for example. Probably still lose a lawsuit, though.