You shouldn't have an adjustment disorder if you have PTSD, because you wouldn't be able to tell whether the anxiety, depression and mood was due to the new issue, regardless how minor or major, versus PTSD itself being the cause of the symptoms due to a new stressor presenting.
This is where the differential diagnosis comes into play that is from the DSM V [DLMURL="https://www.myptsd.com/c/articles/adjustment-disorders.4/"]Adjustment Disorder diagnosis[/DLMURL]:
With regard to symptom profiles, an adjustment disorder may be diagnosed following a traumatic event when an individual exhibits symptoms of either ASD or PTSD that do not meet or exceed the diagnostic threshold for either disorder. An adjustment disorder should also be diagnosed for individuals who have not been exposed to a traumatic event but who otherwise exhibit the full symptom profile of either ASD or PTSD.
See the part about meeting or exceeding the diagnostic threshold for either ASD or PTSD.
Based on your question there is one instance only where this would exist, however; it wouldn't exist as you have stated, being both together.
You can be diagnosed with PTSD, recover, and no longer meet the diagnostic criterion. Once you no longer meet the diagnostic criterion from recovery, you no longer have PTSD. Its like a broken bone... you broke it, it healed, you don't still have a broken bone, you have a history where you broke your bone. It is the same with mental health... in that once you no longer meet the criteria, you no longer have the disorder.
So you could have been diagnosed with PTSD, fully recovered with no ongoing issues... then later in life you have an event where the symptom profile meet adjustment disorder but not ASD or PTSD... thus you don't have both, you just have adjustment disorder at that time in your life. Again, once it has gone... no further diagnosis exists.
Outside of this you couldn't be diagnosed with both, because diagnostic medicine states that you choose the most severe within the spectrum presented. Both PTSD and adjustment disorder are trauma and stressor disorders, thus you can only be diagnosed with one or the other, but not both at the same time due to diagnostic application. If you started with adjustment disorder and it developed worse, then that is dropped and replace with PTSD, but not both simultaneously.
Because PTSD was an anxiety disorder, that precluded other anxiety disorders being diagnosed, such as social anxiety if symptoms increase in social situation, so forth... where now, technically, you could be diagnosed with PTSD + other anxiety disorders, because they no longer sit within the same heirachy and are considered different via categorisation.