Can Cirrocumulus and Cirrostratus appear at the same time?
Clouds don't really form in a fully stable atmosphere, so the distinction between &quot;stable&quot; and &quot;unstable&quot; is not real here. An approaching warm front in particular offers many types of clouds, and among other types one may well see high-altitude cirrus, cirrocumulus and cirrostratus clouds appearing together.
Beach weather approaching ... but first:
Wikipedia  gives the following description of the wide variety of clouds that may appear in the case of an approaching warm front.

Cirrus, cirrostratus, altostratus, nimbostratus, then stratus. Other clouds can also often be seen, including cirrocumulus amongst the approaching cirrus, altocumulus with or instead of altostratus (particularly if the front is weak), and occasionally cumulonimbus along with or instead of nimbostratus in summer. Additionally, stratocumulus often appears underneath the main altostratus deck and stratus fractus typically forms in precipitation falling from the thick nimbostratus layer. Often in warm temperatures, rain bearing cumulus congestus clouds can appear under the cirrostratus, and more rarely altocumulus castellanus clouds if convection is sufficient. In cold humid conditions, low airmass stratus or fog may obscure the main frontal clouds.

A picture from the article, showing the major cloud types:

Source: https://commons.m.wikimedia.org/wiki/File:Warm_front.svg#mw-jump-to-license. By WP user Kelvinsong.  License in link.
We see that the cirrus and cirtostratus clouds are adjacent, and from the table entry quoted above that cirrocumulus clouds can appear among the cirrus clouds.  Since in reality some overlap will occur between the different cloud regions, an approaching warm front is likely to produce a region where cirrus, cirrocumulus, and cirristratus clouds can be seen together.