Looking at the test suite:

* read1() of LZMAFile and GzipFile (both implementing BufferedIOBase) are asserted to return a non-zero result until EOF
* LZMAFile.read1(0) is asserted to return an empty string
* BufferedReader.read1(-1) is asserted to raise ValueError
* There are also tests of read1() methods on HTTPResponse and ZipFile.open() objects, but those methods are undocumented

It seems the most consistent way forward would be to:

* Define BufferedIOBase.read1(-1) to read and return an arbitrary number of bytes, more than zero unless none are available due to EOF or non-blocking mode. Maybe suggest that it would return the current buffered data or try to read a full buffer of data (with one call) and return it if applicable.
* Change the signature to BufferedReader.read1(size=-1) and implement the size=-1 behaviour