I can do three months (or four) before I start. I have one data base search to finish, and then I can go back to the firms I queried in the beginning. There are also some agents I passed the first time through because they wanted some customized, longer query letter, a process I thought I'd skip if I could. By the time I get to those places that I queried two months ago, more time will have passed.
Or, who knows, maybe I'll have representation by that time. I do have people looking at my book. I just like to keep busy while they do so, rather than obsessively check my inbox!
However, I don't know that I would get an "assistant sorts and sees the same query" problem, because I have largely emailed. My older queries were also before I responded to some comments by agents and shortened my book, changed the query, and even changed the name of the book.
(I've kicked around the idea of requerying folks who have rejected me, or not responded after months, with my new query, but I don't know if that would accomplish anything. I've only requeried those that gave me some indication that my rewrite might change their mind. I picked up a couple who are willing to look at my writing again so I guess that wasn't wasted effort.)
I guess I shouldn't have joked about being rejected twice by the same agent. I accidentally queried the same agent twice, but months apart and with two different query letters. I do keep a list but for some reason I didn't see her name until I was checking later for someone else. Too embarassing to email and say, "Never mind ..."