Sam, Rav Ariel Cherlow of Yeshivat Petach Tikva has a discussion of this issue at edited, no links please.
In summary, there are a number of reasons to not only prohibit asking another rav but to prohibit him from allowing what the first rav disallowed such as the first rav’s honor, the fact that the questioner accepted whatever pesak would be given, the fact that it was as if he assured the action or the item 9shavia anafshei k’chaticha d’issura) although there are some instances where it is possible such as a rav who made a mistake in halacha pesuka (taah b’devar Mishna), there is a clear messoret against the pesak or there is the possibility of an appealate proceeding (this would seem to be limited to dinei mamonot).
BTW, once a couple in Vilna had a chicken question. The husband asked the av bet din, who paskened kosher, but while he was away the wife asked the Gra, who lived in their court, who paskened the opposite. When the husband told the av bet din, he said “with all due respect to the Gra, I am the av bet din and the Halacha in Vilna is like me. Tell the Gra that your wife will serve the chicken for dinner and he will join me there”. The Gra, in his great anava, agreed but when the wife served his portion she knocked over a chelev candle onto it. The Gra said “of course it is kosher as the av bet din paskened but I made it assur to myself so I was prevented from eating it”.(Rav Maimon, “Tolodot HaGra”)