Argentine default: "Rights upon future offers" Argentina defaulted on its sovereign debt in 2002. It has reached an agreement with most but not all of its creditors. Wikipedia has a pretty good summary. The agreements included a 70% hair cut but also a RUFO or "Rights upon future offers" clause stating that if in the future agreement is reached with the holdouts with better terms (lower loss percentage) those better terms automatically apply to the creditors signing the current agreements. (This is similar to a most preferred customer clause.) Perhaps the Argentine government used this as a negotiation tactic as it makes it impossible to offer better terms to the holdout creditors.

Unfortunately the holdouts bought a lot of CDS insurance and now stand to win more from a default then they do from a 100% repayment. Lawsuits lasted for years. Argentina made payments to the creditors it agreed with but made no payments to the holdouts. In 2014 (maybe 2015) a court blocked payments to the non-holdout creditors because you cannot differentiate between identical bonds in case of default. This is plunging Argentina into default again which is bad for the country and the creditors with whom it already came to an agreement. (There is another court hearing scheduled for April 2016 and the US government is advocating in favor of Argentina.)

Why haven't the non-holdout creditors and Argentina signed a new agreement in 2014 without the RUFO clause but identical in all other ways? Seems like both of them would have benefited from it, just as they have by coming to an agreement in the first place. (I am not necessarily looking for the 'exact' or 'real' reasons. Any plausible reasons that make economic sense are fine.)
This is a good question! It turns out that exactly as you predict, if you get the transcripts or recordings from the meetings with judge Griesa in NY, some of the representatives of the non-holdouts said they were willing to sign off on the RUFO clause, voiding it. The logic, as you describe is that this would free Argentina to pay the holdouts, letting Argentina continue its payments to the non-holdouts too, without a risk of the debt ballooning suddenly. This would have saved everybody lots of headaches!

Argentina's government at the time did not pursue this option, perhaps because they saw more political gain in being the victims of 'the US empire's courts' than in solving the problem. The lack of professionalism and interest in solving the problem that their executives displayed during this episode suggests this is the main reason.

Alternatively, it's plausible that they did not pursue this option because they thought that default was so terrible to non-holdout investors, that these would be of help in pressuring the holdouts to accept a lower payment from Argentina in negotiations to avoid default.

In any case, neither strategy worked. The government lost popularity and was kicked out of office, and the new government eventually reached an agreement beneficial to the holdouts.

One, more thing: the Rufo clause actually wasn't such a big deal because it was set to expire soon! So, the non-payment appears to have been a big circus for the Argentinian president then to try to score some points with the more manipulable fraction of that country's population.