We report the discovery by the HATNet survey of three new transiting extrasolar planets orbiting moderately bright ( V= 13.2 , 12.8 and 11.9 ) stars . The planets have orbital periods of 4.3012 , 3.1290 , and 4.4631 days , masses of 0.39 , 0.89 , and 0.49 M _ { J } , and radii of 1.28 , 1.43 , and 1.28 R _ { J } . The stellar hosts have masses of 0.94 , 1.26 , and 1.28 M _ { \sun } . Each system shows significant systematic variations in its residual radial velocities indicating the possible presence of additional components . Based on its Bayesian evidence , the preferred model for HAT-P-44 consists of two planets , including the transiting component , with the outer planet having a period of 220 d and a minimum mass of 1.6 M _ { J } . Due to aliasing we can not rule out an alternative solution for the outer planet having a period of 438 d and a minimum mass of 3.7 M _ { J } . For HAT-P-45 at present there is not enough data to justify the additional free parameters included in a multi-planet model , in this case a single-planet solution is preferred , but the required jitter of 22.5 \pm 6.3 m s ^ { -1 } is relatively high for a star of this type . For HAT-P-46 the preferred solution includes a second planet having a period of 78 d and a minimum mass of 2.0 M _ { J } , however the preference for this model over a single-planet model is not very strong . While substantial uncertainties remain as to the presence and/or properties of the outer planetary companions in these systems , the inner transiting planets are well characterized with measured properties that are fairly robust against changes in the assumed models for the outer planets . Continued RV monitoring is necessary to fully characterize these three planetary systems , the properties of which may have important implications for understanding the formation of hot Jupiters .