Once a dancer moves past the basic chassé, jeté, assemblé step sequences for early nineteenth-century French quadrilles, the very next step sequence I teach them is this alternate dos-à-dos sequence taken from Alexander Strathy's Elements of the Art of Dancing (Edinburgh, 1822). In this sequence the dancer advances moving forward, travels sideways for the actual back-to-back part of the figure, then makes a half-turn to travel forward back to place before completing the turn on the final measure. This is quite beautiful to watch, but the steps are very simple.
I would consider this sequence slightly too elaborate for country dances, which are supposed to use simpler steps.
Here's the sequence:
1b Chassé forward, passing opposite dancer
1b Jeté (left foot), glissade dessous to the right
1b Making a half-turn to face original place, chassé forward, curving slightly
1b Completing the turn, make a glissade dessous to the left and a final assemblé
The counts are "and ONE and TWO, THREE and FOUR, and ONE and TWO, and THREE FOUR." Note that the two halves of the figure have slightly different rhythm patterns. It may help when learning it to clap or chant them several times.
Here's a quick summary of the necessary steps as used above. These are not full descriptions! All of them can be led on the opposite foot.
Chassé: after an initiating hop on the left foot on the upbeat, move the right foot forward, close the left foot behind it, and move the right foot forward again. This move takes one measure ("and-ONE-and-TWO").
Jeté: extend the left foot out directly to the side (second position raised) then, bringing it in front of the right, leap onto it, raising the other foot behind to point straight down, close along the leg. This is a linear "out and in" motion rather than a curving ronde de jambe. The step is initiated on the upbeat and lands on the first beat of the second measure above ("THREE").
Glissade dessous: slide one foot to the side and close the other foot to fifth or third position behind. The slide to the side is performed on the upbeat with the close coming on the downbeat. This is "and FOUR" in the second measure above, where it occupied the second half of the measure, and "and THREE" in the fourth measure, where it takes up the first half.
Assemblé: extend the left foot out directly to the side (second position raised) then hop, bringing the left foot behind the right in either third or fifth position with weight equally on both feet, bending the knees slightly when landing rather than locking them. Again, this is an "in and out" motion. The step is initiated on the upbeat and lands on the downbeat, ("FOUR") in the fourth measure above.