Is there a hidur mitzva after the mitzva is done?

There is a concept of hidur mitzva, which means that we can make the mitzvos we do more beautiful. Examples of this are taking nice esrogim on Succos, getting larger tfillin, getting a megillah written by the best scribe, among many countless others.

The basic level of the mitzva of Chanuka is ner ish uveiso, where the man of the house will light one candle each night for his household. A step up is called mehadrin (beautiful), where the man will light progressively as the holiday progresses. The best is called mehadrin min hamehadrin, which is what most tend to do, whereby each member of the household will light progressively.

The Rambam (a Sephardi) says something most interesting that people don't normally notice, but the Griz (The Brisker Rav) points out that the Rambam says the word Madlik, as opposed to Madlikin, which indicates his view is that there is no such step as the final one we mentioned, that the best mitzva one can do is for the householder to light progressively or recessively, but not for each member to.

This is at odds with the Rema (R' Moshe Isserles, whom Ashkenazi Jews tend to hold like) who holds that each person lighting is mehadrin. So whow are we to understand the Rambam's position, and why does the Rema argue?

We can look to a Gemara in Shabbos that can perhaps shed light on this issue. The context is Bris Milah, where the Mohel realises afterwards that he has left something called tzitzin (small piece of skin). There are two types of tzitzin, the type that leaves the baby boy considered uncircumcised, and the type that doesn't matter. The Gemara concludes that eino chozrin al tzitzin she'einon meakvin, that there is no need for the Mohel to perform the Bris again if it is the type which does not matter.

Rashi explains that this is only on Shabbos that the Mohel doesn't return, but that on weekdays he would. The Rambam says that he wouldn't go back to perform the operation again even on a weekday.

So the Brisker Rav, the Griz, explains to us what the issue really is: after the shaas mitzva is gone, you can't make it better. There is no doubt that this is the case on Shabbos, where everyone agrees that you don't break it for the hidur, but the Rambam sas that once the Mohel is finished the Bris, he can't make it any more mehudar than it was, as the Mitzva has been completed.

The Rema and Rashi disagree, and say that yes, you can! This is the difference with regard to lighting Menoras; The Rambam says that once the householder has lit, there is no hidur mitzva for the rest of the householders to perform a hidur, as the mitzva has already finished when the householder lit the first light, so the hidur stops once he has lit additional lights. Any further attempts at hidur ie mehadrin min hamehadrin are after the shaas hamitzva, so are unnecessary.

We hold like the Rema and Rashi, that we can do hidur after the main mitzva has been completed, which is why each of us lights our own Menora.