Optimal regulatory restrictions on banks have to solve a delicate balance. Tighter regulations reduce the likelihood of banks’ distress. Looser regulations foster the allocation of funds towards productive investments. With multiple banks, optimal regulation becomes even more challenging. Banks form partnerships in the interbank lending market in order to face liquidity needs and to meet investment possibilities. We show that the interbank network can suddenly collapse when regulations are pushed beyond a critical level, with a discontinuous increase in systemic risk as the cross-insurance of banks collapses.