There a plenty of companies providing CRM service apps on Twitter. The way large brands do this and the way CRM service providers do this on Twitter is not through a single account. As an example, if your “Customer Care” app provides a service for multiple companies, each one of those companies should have their own Twitter account. Your “Customer Care” app will DM on their behalf using access tokens acquired through OAuth. Each one of those brand accounts has their own rate limits. Some very large brands will even have multiple Twitter accounts for an individual business unit or product line.
In all likelihood, a single brand’s Twitter account will not reach rate limits unless they are very large (i.e. attcares or ikeausahelp). Many brands have media relationships with Twitter where verification and rate limits can be discussed. That is out of scope of this forum, though.