Yes, it is possible. Evaluate $InstallationDirectory
and from there open the directory $InstallationDirectory\SystemFiles\FrontEnd\StyleSheets. Make there a folder, say, entitled "Custom" and place your favorite StileSheets into this folder. Done. The folder will appear in the Menu/Format/StileSheet.
Later edit: One another way is as follows:
go to $InstallationDirectory\SystemFiles\FrontEnd\StyleSheets. That is, do not evaluate this whole line, but evaluate the $InstallationDirectory
and then go to \SystemFiles\FrontEnd\StyleSheets. There is a notebook PastelColor.nb
in this folder. Hopefully, it is the one you need.
Open this notebook
Go to Menu/Format/OptionInspector. This opens a dialog entitled "Options for PastelColor.nb".
In this dialog identify the pop-down menu "Show option value" and select "PastelColor.nb".
In the Lookup text field type MenuSortingValue. Press Enter.
In the right window of the dialog the item "MenuSortingValue" will be highlighted. As soon as you have no such entry it in the Menu/Format/StyleSheet, you should see the red cross to the left of this "MenuSortingValue" item and "None" to its right.
Click on the cross. It will disappear, and a number will appear to the right of this item instead of None. In my case it was 1100. It is the Menu position of this StyleSheet. In principle, you should have a possibility to change it. However, I tried, but did not succeed. Nevertheless, the postion 1100 is OK.
Press the "Apply" button at the top-right edge of the dialog and then close the dialog.
Save the notebook. Attention: you should not use the Menu/File/Save command or Ctrl+S, but only Menu/File/SaveAs. When you will be warned that such a file already exists, agree to replace it by the new one.
Close the file "PastelColor.nb". Done.
Be aware that the new StyleSheet will not appear in the menu, before you close Mma, When you open it once more, the StyleSheet should show up in the Menu.
Second edit: The menu position of the built-in StyleSheet is most probably blocked for changing.
One else thing that comes into head, you could create your own custom StyleSheet, which would carry all features of your favorite one, but it will be a custom one, and its menu position will be most probably not blocked.
This can be done as follows:
Open a new notebook and define a StyleSheet you typically use, when the PastelColor is not available.
Go to Menu/Format/EditStyleSheet. This opens the notebook "Private Style Definition for Untitled 1".
Go to $InstallationDirectory\SystemFiles\FrontEnd\StyleSheets and open the PastelColor.nb notebook.
Copy-paste the cells defining styles that you you like and use from the PastelColor.nb to the "Private Style Definition for Untitled 1" notebook.
You may also want to add here some other styles, that do not exist in the original PastelColor.nb, but are present in other StyleSheets. It is done analogously, by opening the corresponding StyleSheet notebook and copy/pasting the chosen style from there to your custom one.
Using SaveAs save the "Private Style Definition for Untitled 1" notebook with a custom name, say, "PastelModified.nb" to the $InstallationDirectory\SystemFiles\FrontEnd\StyleSheets directory.
From the notebook PastelModified.nb go to the Menu/Format/OptionInspector. This opens a dialog entitled "Options for PastelModified.nb".
In this dialog identify the pop-down menu "Show option value" and select "PastelModified.nb".
In the Lookup text field type MenuSortingValue. Press Enter.
In the right window of the dialog the item "MenuSortingValue" will be highlighted.
Type there any position between 1 and 1999.
Done. It should appear in the menu. If this also does not work for you, there should be problems with your installation, and I recommend to redirect this question to the Wolfram Supporting Team.