C# Append byte array to existing file

I would like to append a byte array to an already existing file (C:\test.exe). Assume the following byte array:

byte[] appendMe = new byte[ 1000 ] ;

File.AppendAllBytes(@"C:\test.exe", appendMe); // Something like this - Yes, I know this method does not really exist.

I would do this using File.WriteAllBytes, but I am going to be using an ENORMOUS byte array, and System.MemoryOverload exception is constantly being thrown. So, I will most likely have to split the large array up into pieces and append each byte array to the end of the file.

Thank you,

Evan