The above only applies on Shabbos, however if Rosh Hashanah falls during the week, then although the Shofar is permitted to be moved even if one is not doing so for the purpose of using it or using its space, nevertheless it is forbidden to use it and benefit from it on this day. Thus one may not lean a plate on it or use it for other purposes of the like.
Although the Shofar is not Muktzah one may not receive any other benefit from it since the Shofar is designated to be used for fulfilling the Mitzvah of blowing. Thus it may not be used for any other purpose.
Using the Shofar on a regular weekday for mundane purposes:
During a regular weekday one may use the Shofar for mundane purposes. Nevertheless since it is designated for a Mitzvah one must act with respect and not use it for any degrading tasks.
 That one may lean a plate on the Shofar.
 It is not Muktzah being that one is blowing with it that day, and it thus has a status of a vessel designated for permitted use, as was explained in chapter 308/15. [ibid]
Other opinions: The Rashal/Taz [Yoreh Deah 266/1] rule that one may not move the Shofar unless it is needed for the Mitzvah. This is similar to the ruling of the Mila knife that it may not be moved after the Mila is done. [As for why by the Mila knife Admur rules stringently while by Shofar leniently, perhaps this is due to the following differences: 1. The Mila knife is MMC”K while the Shofar is merely MM”I. 2. Blowing is a constant Mitzvah that comes up on Rosh Hashanah, while Mila is a rare occasion. Hence by Bein Hashmashos the knife is still considered Muktzah while on Rosh Hashanah it is considered meant for a permitted use. Vetzaruch Iyun. Likewise Tzaruch Iyun why the Taz/Rashal rule that the Shofar may not be moved for any purpose when seemingly it should at least only be MM”I. Likewise Tzaruch Iyun on Taz Orach Chayim 597/2 towards end which he himself rules that the Shofar on Rosh Hashanah is not Muktzah, and it is only Muktzah when Rosh Hashanah falls on Shabbos. Vetzaruch Iyun Gadol!
 The reason for this is because once the Shofar has been set aside for its Mitzvah it can no longer be used for other matters. This matter is explained in Michaber 665/1-2-see there! [ibid]
 See 586/27