It has to apply to everyone or it doesn't work. Otherwise you would see a massive effective marginal tax level at whatever point it was cut off. (Even if ramped down, although to a lesser extent.) What could be done instead is that the entire tax structure is altered so that much of the cost of the basic income is spread over the entire middle and upper range of income tax brackets, such that the middle class end up in roughly the same situation they were before the GBI was introduced.

That's not basic income. Basic income by its definition goes to everyone. That's what makes it an appealing substitute for minimum wage, welfare, etc.

People usually talk about basic income plus an adjustment in tax and the rest of welfare programs, to make it come out neutral for the average person.