Stack Exchange provides the possibility to do a limited number of API calls per day from the same IP (10,000 if the customer registers the app).
Is it possible to get that number increased?
The 10K limit is not if the customer registers, it is if you register your app and provide the key when you make API calls.
Also, you can get more than 10K per IP if your app authenticates the user and then passes a valid
access_token. In that case, it becomes 10K per logged in user and does not share the 10K IP limit.
From the doc:
If an application does have an access_token, then the application is on a distinct user/app pair daily quota (default size of 10,000). A user can have up to 5 distinct quotas at any one time, though this limit is not reflected in quota_remaining returns for privacy reasons.
If you need more than 10K, per app, calls; chances are that you are doing something inefficiently.
Do you have a specific example, or is this just a hypothetical?
If you can point to a specific, legit app that is being crippled by the 10K quota, then chances are pretty good that people will either point out how it could be done in a less intensive way, or Stack Exchange could be persuaded to adjust the quota (They're often pretty good about such things).