PCGS - I've written before on collecting a seven-mint set of Liberty Head half eagles. In case you've forgotten, the Liberty Head Half Eagle is the only American coin to have been struck at all seven of the mints which produced vintage United States coin designs.
These are as follows:

Carson City "CC": 1870-1893

Charlotte "C": 1839-1861

Dahlonega "D": 1839-1861

Denver "D": 1906-1907

New Orleans "O": 1840-1909

Philadelphia (no mintmark before 1942): 1839-1908

San Francisco "S": 1854-1906
Unless you set ridiculously high standards (like all coins must grade MS65 and finer), this set isn't especially hard to assemble. How about bulking it up with some extra coins that fit the set perfectly and make the set more interesting?

Liberty Head $5, 1891-CC $5, PCGS MS65For the Carson City issues, I'd suggest expanding by seeking to obtain one nice coin from each of the three decades these coins were produced. You'll be looking at three coins, one each from the 1870s, the 1880s, and the 1890s. The first decade is challenging in AU55 and higher, and any uncirculated CC half eagle from the 1870s is very rare. The 1880s date is reasonably easy to locate in circulated grades but challenging in uncirculated. The 1890s date should be available in grades up through MS64. (Total: 3 coins)

Liberty Head $5, 1839-C $5, PCGS MS64The Charlotte issues consist of three types: Obverse Mintmark (1839 only), Reverse Mintmark with Small Letters (1840-1843), and Reverse Mintmark with Large Letters (1844-1861). The 1839-C is extremely scarce in uncirculated, but a nice AU coin should be available. The other two types are more common in higher grades and are pretty affordable in XF and AU. (Total: 3 coins)
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