The emergence of new trading platforms has intensified order fragmentation. Yet, little is known on how this phenomenon affects the behavior of profit maximizing exchanges. I show that fragmentation may allow competing exchanges to retain market power. When order splitting is beneficial for traders, competing exchanges are complements. This leads to non-competitive equilibrium exchange fees. Although trader welfare is higher than under a monopoly exchange, it further rises if order splitting is prohibited. Exchanges are then substitutes and pressure on fees strengthens. Moreover, order splitting discourages exchanges from investing in liquidity enhancing technology, while prohibiting order splitting encourages such investments.