Steelmanning

Steelmanning involves arguing against the strongest possible version of the other side's argument, whether they made it or not. The advantage of steelmanning is that doing it makes a person look like they respect the other side and are brave enough to take on strong arguments; if one's own argument can stand up to or even overcome the steelman of the opposing argument it bodes well. A downside of the steelman is that if the person making the steelman can't stand up to the regular argument the other side is making then they have no hope of overcoming the steelman.

There is no particular name for presenting the strongest version of one's own argument; this is simply standard operating procedure and if a person understands their argument, has anticipated objections to it and can explain it adequately in the time he/she has then there is no reason not to do it.

The opposite of steelman is strawman.