Research in the past several years has boosted the performance of automatic speaker verification systems and countermeasure systems to deliver low Equal Error Rates (EERs) on each system. However, research on joint optimization of both systems is still limited. The Spoofing-Aware Speaker Verification (SASV) 2022 challenge was proposed to encourage the development of integrated SASV systems with new metrics to evaluate joint model performance. This paper proposes an ensemble-free end-to-end solution, known as Spoof-Aggregated-SASV (SA-SASV) to build a SASV system with multi-task classifiers, which are optimized by multiple losses and has more flexible requirements in training set. The proposed system is trained on the ASVSpoof 2019 LA dataset, a spoof verification dataset with small number of bonafide speakers. Results of SASV-EER indicate that the model performance can be further improved by training in complete automatic speaker verification and countermeasure datasets.