As an important fine-grained sentiment analysis task, aspect sentiment triplet extraction (ASTE) aims to identify three elements, i.e., aspect, opinion and sentiment polarity as a triplet. Advanced ASTE researches have mostly explored triplet-wise ability to achieve superior improvement. However, existing models with strong in-house performances may struggle to generalize to the challenging cases with the diverse expression of inter-triplet and intra-triplet elements. To this end, we propose a **M**odel-**A**gnostic **T**raining **O**ptimization (**MATO**) to improve ASTE model inference consistent with expected results facing triplet element diversity. Specifically, we design inter-triplet and intra-triplet metamorphic relations (MRs), and calculate the violation rate (VR) on each element of one triplet through metamorphic testing (MT), indicating the capacity to accommodate the diverse elements. Moreover, we propose an element-wise diversity-aware loss based on the VRs of aspect, opinion and sentiment, which can be jointly trained with existed ASTE models via uncertainty weighing. Conducted on four benchmark datasets and seven ASTE models, experimental results show that our MATO can enhance their diversity capacity, decreasing the average element-wise VRs by 3.28% to 15.36%. Meanwhile, our MATO is comparable to or better than those in terms of F1-score.