Can a encoder mux packages demuxed from a decoder?

[HaujetZhao]

I want to create an output video stream that first remuxes packets from an input video and then encodes frames from another source. The code might look like this:

import av

input_ = av.open('input.mp4')
output = av.open('output.mp4', "w")

in_stream = input_.streams.video[0]
out_stream = output.add_stream(codec_name=in_stream.codec_context.codec.name)

# First, the output stream remuxes packets from the input video
for packet in input_.demux(in_stream):
    if packet.dts is None:
        continue
    packet.stream = out_stream
    output.mux(packet)

# Get some av.Frames from another source (e.g., images, generated frames, etc.)
frames = []
# ... Do some processing to fill the frames list with av.Frame objects

# Then, the output stream encodes frames from the other source
for f in frames:
    for packet in out_stream.encode(f):
        output.mux(packet)

input_.close()
output.close()

Unfortunately, this simple code doesn't work as expected. The output stream doesn't successfully mux the packets from the input stream in the first step.

I know I can use out_stream = output.add_stream(template=in_stream) to successfully remux the packets, but in that case, the output stream will only get a decoder codec, which can't be used to encode the frames in the second step.

So my question is, is it possible to create an encoder that can mux packets demuxed from a decoder, and if so, what modifications should be made to the code?