First you need a conflict detector extension like this
This will give you an idea on which extension has priority over your block.
Then you will have to rework the module that has current priority to extend the other module block logic.
Then if you are overriding the same method(s) you will have to merge logic from both modules into the single method of the module block logic that has priority.
It's not easy and it's not simple. I once worked on a store where the store owner kept purchasing random extensions. I had to deal with a scenario where a controller was overiden three times.
I now try to discourage third party extensions in initial development unless mission critical and defer niceties type extension to phase two of the build.
But also I've learnt to watch for extensions which override a lot and try to avoid using them again in future. Unfortunately that can include avoiding some of the free ones on git. It all depends on whether you can factor the cost of dealing with conflicts in the initial build.
The alternative is to deal with conflicts as part of paid support. But it's unlikely you are going to get sign off from the client if things are still broken in the first phase of the build.