If you only have append access then all you will be able to do is issue a PATCH request without reading the file in advance; doing so is not currently supported by solid-client-js. Instead you can issue the PATCH request directly by calling the fetch function given to you by your session created form the solid-client-authn libraries.
You can see a sample patch request here
Comunica and rdflib.js also supports PATCH requests if you want to use those libraries.