randomized crossover design: one condition repeated twice, need to collapse into one condition

#1
I am trying to figure out the appropriate method of collapsing two of four session conditions for a randomized crossover trial.

We had four session conditions (a, b, c, d) and unfortunately discovered that the same condition was provided twice and we technically only have three unique session conditions (a, b, c/d). For the two session conditions that are the same (c and d), we want to collapse them to create a single session condition (c/d). However, the order each participant/dyad received session conditions in was random i.e. participant 1 could have received treatments in this order: a, c, d, b and participant 2 could have received treatments in this order: c, b, d, a.

We essentially have a session condition that was repeated and two session conditions that were not and decided to include time (i.e. visit) as a fixed effect in the model to account for any visit effects, thus allowing to keep all the data.

Wanted to see if anyone else had other ideas of how to properly account for the session condition that was repeated.

Appreciate any advice!