The Exist site can be modified using Drupal Maintainence. The modification can be new version of drupal installation or it can be installing updated modules or transfering domain contents from server to server or any other things.
Your ready to switch to maintenance mode but you don't want that default look.
You want something custom that matches the rest of your site. These modification are under Drupal Maintainence.

Service Maintenance in Drupal:

By implementing the different requirements set by the client, Drupal Maintanence assure that the enhancements have been added to the existing drupal site, followed by that a secured environment is created. The maintenance department can handle your request by adding some new features related to the theme. Similarly enhancements on the website are done under Drupal Maintenance Services.We make sure that your CMS Drupal Install is up to date, new versions are updated, security updates, theme updated and modules are updated well.

Package Maintanence in Drupal:

Drupal is a flexible open source Content Management System that gives scalable solutions for Website development, website design and theme design. Written in PHP, CMS Drupal gives you freedom to upload your content without any hassle.
Its powerful taxonomy makes it easier to organize and tag your content in a better way. With its power it has become easier to develop and manage Community Websites, Discussion Forums, Intranet Applications, Blogs, Social Media Networking Sites and more.