I asked a similar question on this forum not too long ago. Did you read wendler's article "The world's simplest training template" because he touches on working HIIT into the 5/3/1 template. I'll post a link at the bottom if you didn't or if anyone had similar questions to ours.
As for the twice a day sessions, I can't see why not. I would leave a little in the tank from the first session, as to ensure that you can recover from it in time for the next session, cause id rather perform consistantly twice a day then be sluggish and fatigued for one or the other. That's my view of it, but my knowledge of contioning as it relates to metabolic stress and strength loss is limited, so it'd be best to get a more experienced view on here to comment, figured this may get the ball rolling.
The worlds simplest training template: