Thanks for the detailed response. I've also been reading more about abandoned/withdrawn apps. They seem to have a purpose sometimes.
If you want rights outside the US, you had better get a proper and complete application (whether provisional or real) on file before either of you publishes.
Yes that is the focus here and now.
If provisional #1 never serves as a right of priority to another application and is abandoned ("expired" more accurately, I believe) with no rights at all remaining, provisional #2 can be considered the "first" application anywhere in the world for the invention.
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Oops, bartmans might be right, unless you expressly abandon provisional #1 before filing provisional #2.
Well yes, the idea would indeed be to stop one app before proceeding to next one.
First, you'll have to have a proper and complete application on file (and not abandon it) prior to publication by anyone if you care about rights outside the US and a handful of other countries. For example, in your example, if your competitor publishes before you file provisional #2 (and I'm assuming your provisionals are written as well as non-provisional, real applications), you'll need to maintain the priority date of provisional #1 for rights outside the US.
Second, and more subtly, I don't see why you keep re-filing applications on the same invention.
The main reason is because the invention is changing weekly, almost daily. It was only conceived four weeks ago. A main concern is that if an NPA is filed now, it might need to be changed drastically in a few weeks. Yes it would take care of the UK competitor if he publishes, but the amount of projected NPA revisions seems to be a drawback.
However if a series of provisionals (one abandoned as the next one is filed) will take care of the UK publication, and, allow ongoing revisions easily, then maybe it would acceptable.
After reading about abandoned/withdrawn NPA's, maybe they would indeed be the better route. An NPA filed now would take care of the UK publication concern, and could be withdrawn/amended if major revisions are needed.
If the above is all true, then two determining factors (between provisional or NPA) would be time for first app to be completed (in days), and cost for repeated filings/withdrawals (maybe 10 in six months).
If the improvements are non-obvious, those can be separate applications for the non-obvious improvements. If provisional #1 is adequate to protect the basic idea, it should do. No need for provisionals #2 and #3.
This might apply here. There is one main aspect of the invention which allows it to function, and there are about seven related aspects which help it function better. But without the main part, there is no invention. So maybe this main part can be drawn up first, as you said.
Although, I think the provisional vs. NPA option still applies.