This paper presents an eXtended physics-informed neural networks (XPINN)-based framework for predicting the temperature history during a multi-layer Directed Energy Deposition (DED) process. Advancing from its PINN-based counterpart, the XPINN-based framework demonstrates significant accuracy improvement and enhanced capability of temperature history prediction for more complex parts with domain decomposition. It is validated via a series of benchmark tests against ANSYS simulations with increasing degree of complexity. The effect of different domain decomposition is compared and commented on. Strategies that improve the training outcome are also proposed and analysed. The proposed framework brings process-ware design optimisation based on scientific machine learning (SciML) techniques one step closer to the application to real-life engineering applications.