Sandwiches as we know them have been around quite a while and though humans have been eating food on bread for centuries, the Earl of Sandwich made the idea of two pieces of bread the standard. Nowadays we think of the club sandwich as a three-slice affair but some of the earlier recipes for Club Sandwiches, by name, don't necessarily call for more than two.
What does seem to distinguish club sandwiches from contemporaneous sandwiches is a filling featuring more than one sort of meat: bacon, lettuce, tomato and sliced turkey or chicken, sometimes tongue or ham. From the later 1800s into the twentieth century most sandwich fillings presented in cook books seem to have been mixtures: cheese blended with another ingredient, or a salad of chicken, or tuna fish, or eggs. Lettuce was often laid on the salad filling, too, and the bread was sliced thinly. These sandwiches seem to have often been dainty fare for tea but heartier sandwiches had been offered for a couple of decades before in bars. A club sandwich, with its robust filling, however, seems masculine. The name certainly implies that the sandwich was to be found at gentleman's clubs. One 1909 recipe in The Good Housekeeping Woman's Home Cook Book, Chicago, by Isabel Gordon Curtis says "complete this delicious 'whole-meal' sandwich with the remaining slice of toast." A whole meal in a sandwich was a far cry from little tea sandwiches beloved of ladies.
In the first decade or two of the twentieth century, there probably were overlapping practices in club sandwich construction, as a quick look shows sandwiches called club with only two slices of bread. Lowney's Cook Book, 1907, Boston, page 199, has a two-slice club containing tongue, lettuce, and tomato with mayonnaise. Lily Haxworth Wallace's Rumford's Complete Cookbook, 1908, basically calls for a BLT with sliced chicken and two slices of bread.
An example from The Neighborhood Cook Book compiled by the Portland Section Council Of Jewish Women. Portland, OR. published in 1914, is named "Li Hung Chang Sandwiches," and goes like this: "One slice of white bread, one slice of rye bread; butter each slice, place on the white bread the sliced white meat of either chicken or turkey, on top of this two slices of smoked beef tongue; if desired one or two pieces of bacon may be placed between the white meat and the tongue; cover with the rye bread, trim away the crust and cut through diagonally." (pg 282.) Li Hung Chang was a famous Chinese general and statesman who had died in 1901, though since I don't know the context for this reference, his connection to any sandwich at all puzzles me.
From the same cook book comes this three-slice sandwich called "Club House Sandwiches." "Toast thin slices of white bread, butter lightly and place on them thin slices of crisp fried bacon. Lay on another slice of buttered toast, then slices of chicken well seasoned, another slice of toast and then cucumbers, pickles sliced crosswise and another slice of toast. A third one from Portland called "club" called for only two slices of bread.
I'd love to see Mrs. Rorer's 1894 sandwich cookbook, to see if three-slice clubs appear there or if they are all two-slicers. From my own reference collection I can't detect when the tipping point is to a three-slice club. Not until after the 1920s, I am going to guess. It would not surprise me one little bit if something like Howard Johnson's restaurants or a similar phenomenon codified the three-slice club sandwich. It bears more research.