CCMP Capital Advisors and GS Capital Partners might get bested in their efforts to acquire Triad Hospitals Inc. (NYSE: TRI). The two firms agreed on a $6.4 billion buyout last month (including $1.7 billion in assumed debt), but Triad was free to solicit superior proposals for next 40 days. And it may have found one, according to a Wall Street Journal report that Community Health Systems (NYSE: CYH) is nearing an agreement worth “several hundred million dollars” more than the existing offer. If Triad were to accept the CHS proposal, it would owe CCMP and GS a $20 million breakup fee and another $20 million in reimbursement for out-of-pocket expenses. Lehman Brothers is advising Triad on the sale.