Yes, it would be possible...

The form is defined by the extension in the frontend/specialpages/actions/RequestAccount_body.php [1] Thus, it would be preferable to find work-arounds rather than customize the code in the extension to actually add additional form elements; since that would hinder our ability to upgrade the extension (unless of course we could get our customizations published into the next version of the extension).

So, the easiest/best option would be to use the "Notes" field to ask the user to explain "What edits or new articles do you think you'll make to the Slicer wiki?". Through manipulation of the user interface for this existing field, we can change the text elements associated with the 'notes' field.

In short, we can edit the interface elements at http://wiki.slicer.org/slicerWiki/index.php/MediaWiki:Requestaccount-notes and http://wiki.slicer.org/slicerWiki/index.php/MediaWiki:Requestaccount-ext-text

See the attached screenshot of the http://wiki.slicer.org/slicerWiki/index.php/Special:RequestAccount Request Account form.

NOTE: The "Terms of Service" form option (currently shown on the form) should either be disabled, or else there should be a working link (content needed) for "Terms of Service". In short: we have no terms of service, but we force users to "agree" to the TOS in the account request.

Also, for documentation purposes, the way the "Confirm Account" system works, under our configuration, Users in the group "Administrators" (sysops) will receive an email notification of account requests. They will also see a notice of pending account requests whenever they login to the wiki. Any unreviewed account requests are automatically marked as "rejected" after one month ($wgConfirmAccountRejectAge [2]). Rejected requests are deleted after a week ($wgRejectedAccountMaxAge). All account request data is stored in the database and can be viewed by Bureaucrats.

[1] form definition https://phabricator.wikimedia.org/diffusion/ECAC/browse/master/frontend/specialpages/actions/RequestAccount_body.php?color=1
[2] variables that can be overridden in LocalSettings.php
https://phabricator.wikimedia.org/diffusion/ECAC/browse/master/ConfirmAccount.config.php?color=1

I've updated the text displayed in the "Other information" section of the form.

http://wiki.slicer.org/slicerWiki/index.php/Special:RequestAccount

The need for "Terms of Service" content should probably be broken out into a separate issue.

Thanks Greg for the detailed explanation.

Looks great. I am resolving the issue.

I will let Andriy close it.

Looks much better, thank you!