Can a prosecutor add additional charges to pressure a defendant to plead guilty to the original charges?
There is a tort of malicious prosecution which could be relevant: if the prosecutor knowingly and with malicious intent charges a person. The prosecutor has to have probable cause for the charge, meaning that a reasonable person would believe that the accused committed the crime. A prosecutor cannot maliciously prosecute a person. Acting to obtain a guilty plea is not malicious intent, per se.
In the US, there are often multiple laws against an act, and there can be multiple counts of violations of a specific law. A prosecutor can legally add charges, for example adding criminal trespass and assault to a burglary case. Adding a rape charge (in the normal circumstance) would be malicious prosecution, and not allowed. The cumulative penal risk arising from conviction on burglary, assault and criminal trespass might be enough to convince a guilty person to plead guilty on a single charge.
The prosecution is, in general, allowed to modified the state's claims against a person, so they can add and drop charges based on numerous considerations. There is no requirement that the prosecution file all tenable charges or forego the option of later adding charges.
A prosecutor can only charge a defendant with crimes they reasonably believe they can gain a conviction for
A prosecutor is an officer of the court, they have a primary duty to justice - not to gaining convictions.