**** UPDATE Feb 2021 *** Please read the comments to this response. Their general conclusion seems to be that some web servers accept multiple Authorization schemes, but that it goes against RFC 7230/7235 ****
This should be possible, you just have to add a comma between field values, e.g:
GET /presence/alice HTTP/1.1
Host: server.example.com
Authorization: Bearer mF_9.B5f-4.1JqM, Basic YXNkZnNhZGZzYWRmOlZLdDVOMVhk
This is defined in RFC7230, section 3.2.2, Field Order:
A sender MUST NOT generate multiple header fields with the same field name in a message unless either the entire field value for that header field is defined as a comma-separated list [i.e., #(values)] or the header field is a well-known exception (as noted below).
A recipient MAY combine multiple header fields with the same field name into one "field-name: field-value" pair, without changing the semantics of the message, by appending each subsequent field value to the combined field value in order, separated by a comma. The order in which header fields with the same field name are received is therefore significant to the interpretation of the combined field value; a proxy MUST NOT change the order of these field values when forwarding a message.
I don't know whether all web servers accept this - at the time of writing I'm in the middle of a debate with a colleague about whether it should work or not.
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