It's possible that Elon musk wants to make more money from the market, but I doubt. I feel he's only trying to entertain himself and he has a personal affection for dogecoin and wants to support the coin. It could be that due to the fact that the meme coin has been related, he was to bring it to limelight.
His real intention is not yet clear. He doesn't own any cryptocurrency directly, so we can't claim that he is benefitting (at least personally) from the movements in the market. But at the same time, I have my own doubts. If you carefully look at his tweets, a clear pattern can be observed. The manipulation he did was well planned and made use of his millions of social media followers. Now looking back after a month, it is difficult to believe that Elon is innocent and he just wanted to promote some shitcoin for fun.