Here's what I can determine from the books I cite here:
Condos Brothers Bibliography
Books are noted below by author's initials, as keyed on the bibliography.
I've seen all this information elsewhere too; just wanted to cite some edited, published books.
This timeline is intended to justify 2 things: that the brothers in The Midshipmaid (1932) were Frank and Nick, and that the brothers in all subsequent films were Nick and Steve.
From [CH]: Frank was born 1906 in Greece; Nick, 1915 Philadelphia; Steve, 12Oct1918 Pittsburgh.
From [BS]: Frank first partnered with a non-family member as professional dancers; they split. In 1929, Frank forms duo Condos Brothers with Nick. In 1930, they earned praise in the Broadway show Earl Carroll's Vanities. They performed in London and Paris (with the show?)
Note: The Midshipmaid was released in 1932.
Frank splits with Nick in either '33 [CH] or '36 [BS].
[All] Steve partners with Nick as the Condos Brothers.
From [RF], quoting Steve: "I was 14 years old when I went into show business... But I wasn't any good!" Then he describes how he practiced, took the advice of other performers on how to improve. The other live acts he sees/is on the bill with. And then...
[All] Nick and Steve, as Condos Brothers, make films.
On the bibliography you can see which films were mentioned by name. But nowhere does it say that Frank joined them or substituted for one of them. Nor do any of these books mention "Harry," currently credited on several IMDb listings.
But "Harry" is not strictly an Internet invention. On the 1930 Playbill (viewable online) for the Vanities, the 2 brothers are listed as Frank and Harry. Why? Haven't found an answer. But perhaps, since films sometimes list credits with wrong/misspelled names, perhaps even Broadway listed a credit wrong in a Playbill from time to time.
For visual evidence, please see my post Condos Brothers Clips and Screenshots. The screenshots are mostly title cards with Condos credits, but include 2 of the brothers in The Midshipmaid (1932). Enjoy the video clips while they last; some studios are very strict about copyrights.
I'll start submitting edits to IMDb pages now.