Council of Elrond

If I play a card that removes the limit on how many characters I can play (such as Sauron or An Unexpected Party), can I also reveal my avatar or discard a character during the same Organization Phase?

Cards like Sauron or An Unexpected Party remove the normal limit on playing one character per Organization Phase; for reference, here is their text:

SAURON ‐ Permanent‐event
Manifestation of The Lidless Eye. Playable if your opponent is a Wizard and you have not revealed a Ringwraith. You are Sauron, not a Ringwraith. You may not reveal a Ringwraith or play Ringwraith followers. +10 to your general influence. Discards and prevents the subsequent play of Bade to Rule. During your organization phase, you may bring a resource or character from your sideboard into your play deck and shuffle and there is no limit to the number of characters you may bring into play. Cannot be duplicated. [Cannot be included in a Balrog’s/Fallen-wizard’s deck.]

AN UNEXPECTED PARTY ‐ Permanent‐event
Only playable during the organization phase on a company. There is no limit to the size of this company. Dwarves with a mind of 2 or less in this company do not require influence to be controlled; and there is no limit to how many Dwarves may be brought into play on a given turn with the company. Discard this card if the company has more than one non‐Wizard character with a mind greater than 5 or more than two non‐Dwarf characters or no Dwarf with a mind greater than 5. Cannot be duplicated on a given company.

Importantly, the normal rules for the Organization Phase allow a player to either play a character (whether an avatar or a non-avatar) or discard a character from play. From the CoE rules:

2.II.2 Organizing by Playing (or Discarding) a Character - The resource player may play or discard a character while organizing during the organization phase. This action can only be taken once per turn.

And for reference, from the MELE rulebook:

During your organization phase, you may perform one and only one of the following activities:

• You may play a non-Ringwraith character card. …
• You may play a Ringwraith card if you do not have one in play. This is called «Revealing your Ringwraith.» …
• Instead of bringing a new character into play during your organization phase, you may discard a character that is at a Darkhaven or at his home site.

Since revealing your avatar counts as playing a character for this allowance, removing the limit on how many additional characters may be played would mean that you are allowed to reveal your avatar and then also play additional characters during the same Organization Phase per the effects of either Sauron or An Unexpected Party.

However, you still must first choose to either play one character or discard one character, so if you choose to discard a character from play with the normal allowance, you are not allowed to then play additional characters with Sauron or An Unexpected Party because those cards merely remove the limit on how many characters can be played (and if you’re choosing not to play one character, then removing the limit doesn’t provide any additional allowance to then play more characters). Furthermore, if you choose to discard a character, a card like Sauron would not allow you to discard additional characters because the limit being removed is specifically for playing characters, not discarding them.

There is no limit of how many Dwarves may be brought into play on a given turn (with some company or at all) as there is no limit of how many Elves may be brought into play on a given turn.
An Unexpected Party addresses a limitation that does not exist.

I think that proper way of dealing with the problem is a correcting of text of An Unexpected Party in such way that it will reflect supposed intention of authors (or intention of corrector).

E.g.

"Only playable during the organization phase on a company. There is no limit to the size of this company. Dwarves with a mind of 2 or less in this company do not require influence to be controlled; if you are bringing a new character with the company instead of one character you may bring any number of Dwarves. Discard this card if the company has more than one non‐Wizard character with a mind greater than 5 or more than two non‐Dwarf characters or no Dwarf with a mind greater than 5. Cannot be duplicated on a given company."