At over 1,300 pages the Scott Specialized Catalogue of United States Stamps and Covers is the most comprehensive catalog for U.S. philatelic material. However, Expertizing still relies on other catalogs for more specialized listings of certain types of U.S. material.
Bureau precancels may be listed in Scott when they vary from the regular U.S. listing because they do not have tagging. However, the Precancel Stamp Society (PSS) Bureau Precancel Catalog and Town and Type Catalog go into much greater depth. The latest edition of the Bureau catalog lists 9,421 stamps precanceled by the Bureau of Engraving and Printing and the Town and Type catalog lists 42,502 precancel types from 21,350 towns. The PSS offers about a dozen additional catalogs, many of which are available in traditional printed format, as pdf files or even as computer databases. Full details are available at https://www.precancels.com/publications/
One of the other PSS catalogs is of perfined precancels of the United States which is related to another area where sometimes a more specialized catalog is helpful, usually the Catalog of United States Perfins published by the Perfins Club. Most precancels and perfins are probably less valuable than the base stamps, but there are always exceptions. Different companies used the same combination of letters for the perfins so the actual hole patterns may be necessary to differentiate the companies.
Another catalog of U.S. stamps that is often helpful in determining exactly what you have is the Durland Standard Plate Number Catalog published by another APS affiliate, the United States Stamp Society. Some collectors may use it to try to find scarce plate blocks available in dealer face value boxes or lots. However, for expertizing if there is a plate number on a stamp with a design such as a Washington Franklin with many different catalog numbers, the plate number may help you narrow down the possible Scott Catalog numbers or cause further review if the plate number does not match those listed for a specific catalog number.
Pages from the Durland Standard Plate Number Catalog
Probably the most common example where non-Scott numbers are used on APEX certificates for U.S. material (normally in addition to the Scott number) is postal stationery. The United Postal Stationery Society has over 20 catalogs (including some titles for foreign philatelic material). By far the two most commonly consulted are their Catalog of 19th Century Stamped Envelopes, Lettersheets and Wrappers of the United States and their Catalog of the 20th and 21st Century Stamp Envelopes and Wrappers of the United States.
These catalogs go into much more depth than the US Specialized with different catalog numbers based on watermarks, envelope size and knives. In addition to the different color shades of the paper, for 19th century U.S. stamped envelopes there are 19 different sizes of envelopes, 13 different watermarks, and over 100 different knives or envelope cutting forms which can vary not only in shape but also in how the envelopes were folded such as whether the bottom of the envelope is over the sides or the sides are over the bottom. The books also include color charts for United States stamped envelopes and wrappers.
One final catalog regularly used by our expertizing service is United States Cancellations 1845-1869 by Skinner and Eno which illustrates (but does not value) fancy cancels by city of use.
Entire books exist that provide more detail on specific U.S. issues, but beyond catalogs the most common book we use for expertizing U.S. stamps is R. H. Whites Encyclopedia of the Colors of United States Postage Stamps -- which unlike the previously mentioned catalogs is out of print (and when available, usually expensive).
Pages from R. H. Whites Encyclopedia of the Colors of United States Postage Stamps
The above is not comprehensive. Occasionally specialized catalogs are consulted for areas ranging from first day covers to tagging (the phosphorescent coating incorporated on U.S. stamps to allow for facing and cancelling of envelopes by machines). Many of us own odd items for which acquisition of specialized literature may not make sense, but collectors with specialized interest should certainly consider membership in related APS affiliates (we have over 180) and the publications they often publish.