You can record a conference call at Plivo in two ways 

Using record API:

The Record API can record live calls at any time during the call and returns the URL of a file containing the audio recording.

For more details: 

To get the callUUID of the conference call which is ongoing so as to record the call, you can make use of this API 

Using Record attribute in conference XML:

You can use the ‘record’ attribute by setting it to ‘true’ in the conference XML so as to record the conference call.

For example: 

    <Conference record="true">My Room</Conference>

You can also setup the recordFileFormat as either Mp3 or Wav.

For more details: