What is a "versatile" gown?
For a more detailed analysis of this gown and other layers worn by women in the art of the late 14th and early 15th centuries, see my paper, How I learned to stop worrying and love layers. This paper also contains a bibliography of sources used during the development of the thoughts that follow. Although not exhaustive, that list is a great starting point.
One encompassing trend in the fitted styles portrayed in this period's art is the fashionable layering of gowns, specifically two: a gown and an overgown. The construction of clothing, whether made for nobility or by the common man, was a labor-intensive task, and people generally had less items in their wardrobes than perhaps the current-day person who can buy off-the-rack has. This would necessitate the coordinating of fashion layers with as much versatility as possible. Another possible factor for the careful combining of fashion layers may have been the cold weather which was not nearly so avoidable indoors in those days as it is today.
Based on my research into the fitted gown styles of the late 14th and early 15th centuries in Europe, I have come to the conclusion that women wore a basic gown for daily living that in some cases also doubled as a solo fashion layer or could be worn with another fancier layer atop it. I named this gown the "versatile" layer as a descriptive catch-all, given how many possible terms for this garment exist in the written texts from the period — none being completely definitive or all-encompassing.
The versatile gown could be tailored a number of different ways. For busts needing support, it appeared to require tight fitting through the upper torso. I am fairly certain that this gown existed in a pullover form as well, given how often it is portrayed without any visible signs of closure in the period art and the fact that some body types can achieve bust support with a closely tailored pullover gown. In my initial forays into this subject, I wondered if the chemise (the "underwear" layer) may have provided bust support in addition to this first fashion layer. In correspondence with Robin Netherton, however, I was convinced to take a closer look at the art of the time for my answer. I found that in pictures where chemises are visible, as in nursing scenes for example, the fabric of the chemise is often stretched under the breast as a solid panel. It does seem possible that the neckline might have had a slit in it on occasion, but I now doubt that chemises were routinely laced-up. The bust support, if there at all, probably came from the first fashion layer on top of the chemise. In more cases than not, that gown was versatile in nature, at least as portrayed in readily-available period images.
What specifically makes a gown versatile is the combination of closure and sleeve style elements that allows for the layering of another fancier overgown. Though there are examples of gowns in the art of this period where buttons are used down the center-front opening of gowns with long, close-fitting sleeves, these styles are limiting and do not fall within the parameters of versatility. Why? Because buttons on the torso would poke into the body should a close-fitting overgown be worn atop it. Also, unsightly bumps or a ridge may appear through the fabric of the form-fitting overgown, and that is something I have yet to see in my ongoing perusal of this period's art. There are examples of a buttoned gown worn beneath a loose overgown, but I have not come across definitive evidence for such where the fancier overgown was form-fitting. If a gown is a pull-over or has lacing somewhere on the torso (most likely the center-front with side-lacing as another option seen in the period's art), it lends itself naturally to the layering of another gown atop it.
In addition to torso closure treatments, consider sleeve styles and how they affect the layering of gowns. The button-front gown with long, fitted sleeves is limited as a solo fashion layer because not only is it not able to attractively or comfortably accomodate another gown over it, another gown can't be worn under it due to its long, tight sleeves. Close-fitting, long sleeves, in and of themselves, go well on gowns designed to be worn alone and with fancier overgowns. They can easily be pushed through loose or voluminous sleeves of some kind. Popular styles seen in the art of the period include bag sleeves, "angel" sleeves, or loose tube sleeves. Another popular overgown sleeve style is the short sleeve, with or without decorative flaps or tippets — bands encasing the ends of short sleeves with a decorate flap hanging off the end. Gowns with these sleeve treatments are limited to their roles as fancy overgowns, since their sleeve styles make it unlikely that another fashion layer could be worn atop them.
All of these descriptions without visuals may seem confusing! Here are some simple drawings to give you an idea of what a typical versatile gown might look like when worn solo (left) and what it might look like when worn under a fancier overgown (right):


Note that the sleeve treatment of the overgown is universally designed to show off some portion of the versatile layer's sleeves. The complimentary nature of the versatile gown and the fancier overgown is rather consistent in the period art.
A popular style seen in many historical costuming circles is something that is often called a "cotehardie". I put this term in quotations because we have no first-hand proof that it was applied in period to the gown it so often represents here and now in re-creation forums. Here is what this gown usually looks like:

More questionable than the term used to name it is the likelihood of its popularity in the time period it purports to represent. When held up to versatility standards, it fails, as it is restricted as the sole fashion layer worn over a chemise. The buttons down the center front preclude another gown layer over it, and the long, tight sleeves mean that it can't be a fancy overgown either. Perhaps the lack of fashion layering options is why this style is rather uncommon in the period art and by extrapolation, possibly less commonly worn in period. That said, there are some instances of center-front buttoned gowns with long, close-fitting sleeves without buttons (in the Bible of Wenceslas IV, for instance, which can be seen in Olga Sronkova's Gothic Fashions in Women's Dress). This close cousin of a style would be equally ungainly as a versatile layer. There is also one English funeral brass that I have seen clearly portraying the so-called "cotehardie" style — buttons on long, tight sleeves and up the center-front (Eleynore Corp, c. 1361 or 1391, depending on the source), but it stands alone, so far in my search.
So how could this style have become so popular in current historical costuming circles? It is attractive, no doubt, and we are often susceptible to seeing pretty gowns worn by others and picking up that idea or "look" and perpetuating it. As modern-day people, we also do not tend to think in terms of wearing two dresses, one on top of the other. It may never occur to us that stylistic elements such as buttons or sleeve treatment could limit us in a period fashion environment. Finally, there is the issue of equating masculine fashions of the period with female fashions. Men often did wear short cottes with buttons down the front and up the sleeves. Simply extending that look to the floor would certainly produce an attractive style, but not one that is gleaned from a period source if that is one's reasoning. Back-documenting this gown is more challenging that one would suspect, given how popular they are to re-create.