Right pattern to be used in situation where some handlers are independent and some handlers depend on other handlers execution

Working on redesigning a system which compute some attributes given input as an object like property.

We are using handlers to compute property related attributes. Each handler takes care of computing single property attribute information.

Problem: 1. There are some handlers which depend on other handler's output (other attribute to be computed first).

Proposed Solution: I was thinking to use CoR (Chain of responsibility pattern) here. My idea was to use CoR only for the handlers which depend on each other's output. will invoke other handlers independently.

Is there any other pattern or better way to get the done ?

Don't want to use CoR overall because might in future we will want to run these handlers in parallel which is not possible if i use CoR pattern here.