The multiplier effect can work both ways, even if you paint it as the villain and one context and the savior in another. You're suggesting that an extra dollar in the pocket of a rich man is worth more to the economy than an extra dollar in the pocket of a poor man. But that theory has never been proven either way.
The way I see it that extra dollar in the rich mans pocket leads to productivity down the chain, thus keeping the economy moving at multiple levels.
The extra dollar in the poor mans pocket nets you no return productivity.
And what happens when the poor man uses that dollar to purchase goods and services from the rich man? Does it not lead to productivity down the chain as well?
What happens when the poor man doesn't spend that dollar to purchase goods and services, but instead saves it or pays his mortgage or other debts?