Can collector charge me more than initial debt?

The collection agencies can impose fees and interest rates on the original debt amount. However, they can charge fees and interests only up to a certain limit. Not beyond that. So, it is true that collection agencies can charge more than the original amount.

The FDCPA laws specify how much fees and interest rates collection agencies can charge. Collection agencies can't exceed the cap legally.

This is from the FDCPA: U.S Code 1692f(a)

A debt collector may not use unfair or unconscionable means to collect or attempt to collect any debt. Without limiting the general application of the foregoing, the following conduct is a violation of this section:

(1) The collection of any amount (including any interest, fee, charge, or expense incidental to the principal obligation) unless such amount is expressly authorized by the agreement creating the debt or permitted by law.