Thanks for the update. While you likely have your favorite targets, I think it's acceptable to do this for publishers or agents. Of course, you only want to have the completed work submitted to one editor at a time, but queries needn't be exclusive. I have heard this strategy from numerous pro writers, and used to do this myself. It may be you already have contact with or interest from a specific publisher, which is always the best.
Most agents expect simultaneous queries, so it's almost an unwritten rule.
But I sent the first letter out exclusively because the agency says in their gls that they won't consider simultaneous queries. The agent in question might be eager to work on this project, so I'm trying her first. Check it out. Check it out. Just checking in to see what's new.