Also: if you select two or more hosts where at least one of them have an overridden parameter and at least one of them does not have that parameter overridden and choose 'Edit parameters' in the multi action droplist, this parameter will be presented as if available to edit for all hosts even though not all the selected hosts have an override.

Submitting a new value for the parameter renders the error message
" Host not found. Please try to update your request"

I want my devops to be able to change value on a global parameter. This works fine if you edit the hosts one by one, but since they often operate on hosts 50+ at a time it would be useful to use a filter to show the hosts and then use the multi action droplist to edit the parameters.

Thanks for clarifying the issue, it's definitely a bug IMO, users should be able to update global params the way you described.

As a workaround, you can use hammer https://github.com/theforeman/hammer-cli-foreman / https://github.com/theforeman/hammer-cli to update the parameters, or your own scripts