Exploiting effective target modeling units is very important and has always been a concern in end-to-end automatic speech recognition (ASR). In this work, we propose a phonetic-assisted multi-target units (PMU) modeling approach, to enhance the Conformer-Transducer ASR system in a progressive representation learning manner. Specifically, PMU first uses the pronunciation-assisted subword modeling (PASM) and byte pair encoding (BPE) to produce phonetic-induced and text-induced target units separately; Then, three new frameworks are investigated to enhance the acoustic encoder, including a basic PMU, a paraCTC and a paCTC, they integrate the PASM and BPE units at different levels for CTC and transducer multi-task training. Experiments on both LibriSpeech and accented ASR tasks show that, the proposed PMU significantly outperforms the conventional BPE, it reduces the WER of LibriSpeech clean, other, and six accented ASR testsets by relative 12.7%, 4.3% and 7.7%, respectively.