Can I set AbsTol for only some components of solution?

I have a system of ODEs in matlab which I want to solve using the standard solvers. On some of the values of these components I know sensible absolute tolerances, but on other components this is difficult to determine easily. Is it possible in some way to use AbsTol only for some components of your solution and not others?

I tried setting AbsTol for other components to Inf, or a large value. However this caused issues, I think because the solvers use the values in AbsTol in some way to explore the solution at the start of the computation.