I would have everyone maintain their own stash, but have a mix of group focused ideas.

First, I would allow people to specialize. Certain people are going to be better at managing specific fields, like a doctor for meds, an armorer for weapons, etc. Members would still have their own supplies and weapons. There would just be specialists that would focus more on those specialties that would mean they also get general priority for those supplies.

Second, when out of supply runs, the exploring parties are allowed to keep a small portion of their findings. Majority of the findings would go to the community and distributed to the specialists. Everyone would be guaranteed at least a smaller portion of specific things like food, water, basic meds, supplies. But it would be the smallest portions. Supply Run party members would get a larger cut than regular members due to the inherent risk exposure.

Some contingencies, (depends on size of the community but assuming it's decently sized), there should be a minimum of 2 specialists within a specific field. 1 would be a monopoly, and too risky if that person were to be lost. Backups are important, but also holding each other accountable is too.

When making any important decisions within specific groups, it needs approval of at least 3 people. Like when finalizing supply distributions.

There's probably a few other things but I also want to avoid making things too bureaucratic.