Carl Icahn (April 2013 Forbes cover)

Dinner with billionaire investor Carl Icahn often gives corporate CEOs heartburn. Icahn is known for buying company shares, then pushing for changes – and it is no different with Apple. Monday night Icahn asked Apple CEO Tim Cook to increase to $150 billion the amount of stock the iPhone maker plans to buy back, more than doubling Apple’s previously pledge of $60 billion. Last night’s New York City dinnertime discussion comes after Icahn invested somewhere near $2 billion in Apple in August. Reports say the activist investor sees Apple shares still undervalued…

In a Tweet Tuesday, Icahn described having “a cordial dinner with Tim last night.”

“We pushed hard for a 150 billion buyback,” he continued. The two will continue talking “in about three weeks.”

This is the second time Icahn has prompted potential Apple actions.

A September New York Post report suggested Icahn bought into Apple simply to influence a possible decision to acquire speech recognition software maker Nuance – of which the activist billionaire investor owns 16.4 percent.

If Apple purchased Nuance – rather than develop Siri’s voice in-house – both Apple’s stock and Nuance share value would rise, a win for Icahn. It is questionable whether Apple will increase its buyback plans to a level Icahn wants.

Initially, Apple announced a $10 billion stock buyback in March 2012, then raised it to $60 billion buyback in April as share prices of the company faltered. Remember, that announcement triggered questions about how Apple shuffles revenue around the globe to avoid high taxes.

Of course, Monday’s tete-a-tete between Icahn and Cook may have just been a way to gauge how the other reacts. Can the investor push the Apple CEO? Is Icahn willing to drop more cash on Apple?

For Cook, at least there was no public mention of any leadership challenges. If that were the case, the Apple leader could skip the after dinner mint and go straight to the antacids.