In recent years, many national timing laboratories have installed geodetic Global Positioning System receivers together with their traditional GPS/GLONASS Common View receivers and Two Way Satellite Time and Frequency Transfer equipment. Many of these geodetic receivers operate continuously within the International GNSS Service (IGS), and their data are regularly processed by IGS Analysis Centers. From its global network of over 350 stations and its Analysis Centers, the IGS generates precise combined GPS ephemeredes and station and satellite clock time series referred to the IGS Time Scale. A processing method called Precise Point Positioning (PPP) is in use in the geodetic community allowing precise recovery of GPS antenna position, clock phase, and atmospheric delays by taking advantage of these IGS precise products. Previous assessments, carried out at Istituto Nazionale di Ricerca Metrologica (INRiM; formerly IEN) with a PPP implementation developed at Natural Resources Canada (NRCan), showed PPP clock solutions have better stability over short/medium term than GPS CV and GPS P3 methods and significantly reduce the day-boundary discontinuities when used in multi-day continuous processing, allowing time-limited, campaign-style time-transfer experiments. This paper reports on follow-on work performed at INRiM and NRCan to further characterize and develop the PPP method for time transfer applications, using data from some of the National Metrology Institutes. We develop a processing procedure that takes advantage of the improved stability of the phase-connected multi-day PPP solutions while allowing the generation of continuous clock time series, more applicable to continuous operation/monitoring of timing equipment.