The fact that monetary policy tightening has stronger effects than easing is a longstanding puzzle in monetary economics. This article studies monetary transmission in settings where firms face multiple financing constraints – a common and well-documented feature of corporate financing. Our theory shows that the multiplicity of financing constraints notably dampens the transmission of expansionary policy to firm borrowing and investment, while amplifying the transmission of policy tightening. This asymmetry arises because, when policy tightens, the most responsive constraint binds; whereas, when policy eases, the least responsive constraint limits the expansion of borrowing. We find strong empirical support for these predictions. Moreover, embedding the mechanism in a standard New Keynesian framework, we find that the decline in aggregate investment following contractionary monetary shocks is twice as large as the increase following equally sized expansionary shocks.