lossless: png or tif

The two file format may not make any difference.  First, suppose
Groove Music still existed or there were some way to view an alternate
image in a file.  There is with jpg images which surprises me.  I
found out using Groove Music on a cover for Neverworld's End that I
downloaded from albumartexchange.  So, if I wanted to have two images
in a file, so that I could select an alternate image, which format
would work?