Spoofing countermeasure (CM) and automatic speaker verification (ASV) sub-systems can be used in tandem with a backend classifier as a solution to the spoofing aware speaker verification (SASV) task. The two sub-systems are typically trained independently to solve different tasks. While our previous work demonstrated the potential of joint optimisation, it also showed a tendency to over-fit to speakers and a lack of sub-system complementarity. Using only a modest quantity of auxiliary data collected from new speakers, we show that joint optimisation degrades the performance of separate CM and ASV sub-systems, but that it nonetheless improves complementarity, thereby delivering superior SASV performance. Using standard SASV evaluation data and protocols, joint optimisation reduces the equal error rate by 27\% relative to performance obtained using fixed, independently-optimised sub-systems under like-for-like training conditions.