You can. there are a couple of new 4 seat micro-jets coming on the market in the next year or two that would be priced in the ball park of 1 million. They are not meant to be business jets, as all private jets have been hitherto, but true general aviation jets for private owners like a more spiffy Cessna.
Also, You can get a used business jet from late 1950s or 1960s in airworthy condition for less than a million.
Also, You can get a used business jet from late 1950s or 1960s in airworthy condition for less than a million.