Installation order question

We are replacing two upstairs toilets with Toto models (haven't finalized choice yet). Not doing any other renovation at the moment. Replacement to be done by plumber.

One toilet often loses almost all the water in the bowl; the other toilet never does. It seems to be related to dishwasher use (but not consistently -- could there be multiple factors?) I read on the FAQs that this could be caused by a blocked roof vent.

Would it be better to have the vent issue fixed first, before the new toilets are installed, or does it not matter what order they're done?

[also, may I say I highly appreciate the courtesy and enthusiasm shown on this board, a world of difference from many of the newsgroups, and a credit to you, Mr. Love -- thank you.]

It could be a blocked vent,improperly vented,partial stoppage and is toilet
with the problem 1st or 2nd fl?Also have your installer check it out.Over
looked that both on 2nd fl but all still applies.

Thank you for your reply. When you say "have your installer check it out" do you mean that the plumber could check and possibly clear the vent from within the bathroom without having to go on the roof?

Would it be more likely that we'd need a "roto-rooter" type of service to go up on the roof and work from the top down?

Is there any chance that the roto-rooter type work might damage the toilet or connections in any way, and therefore it should be done before the new toilet is installed?

A reputable company would not damage a toilet during a drain cleaning. If the toilet gets drained, it may not even have a proper vent. That can't always be determined easily without tearing up some stuff. Often, you can tell by looking down the drain while the toilet is off, but not necessarily (that it is vented, not if it is blocked).

I think if I was going to have the toilets installed by a plumber, I'd ask him to try to diagnose and fix any problems while he was there. Course, I'd probably install the toilets myself, but that's another issue altogether.