Is it possible to increase the number of concurrent ad-hoc searches for the user, without increasing the number of scheduled searches?
Yes, you have the number of total searches on the cluster inside limits.conf You could increase that and play with the ratio of ad-hoc vs schedule search. Default is 50/50. I wouldn't do that if you are in a prod env.
You can but with caveats. But before we go there, what's your use-case here for this change?