VaR is a risk metric that applies to individual portfolios. It provides a downside estimate assuming functioning (liquid) markets and a stable financial system / bank intermediaries.
Systemic risk is a feature of a network of large financial counterparties and captures the likelihood that one or more of them will become insolvent due to excessive risk taking.
There is no obvious metric that can be used as the “systemic risk” component of an individual portfolio as you need to work out how each one of your positions is likely to behave in the small probability / high impact scenario where a systemic event is taking place.
Given that the positions of the systemic players are not known in any detail, this is general not possible to do.