In this paper, we analyze the estimation capabilities of IEEE 1588-2008 Precision Time Protocol (PTP) and propose a super-imposed clock timing aware signal exchange protocol over PTP. The proposed protocol, without impacting any existing PTP infrastructure, provides independent clock parameter estimates. In addition, it also provides relative clock phase offset which is not detectable through standard PTP. We demonstrate how the supplementary estimates from the proposed method can be used to improve overall clock synchronization accuracy and also discuss the use of clock phase information in improving PTP event timestamp resolution.