Yes it's possible to unlock your own little version of Dr Robotnik's Mean Bean Machine in Sonic Mania. You'll just need to collect 20 silver medals in order to unlock the Mean Bean mode.
Of course getting 20 silver medals isn't as simple as it sounds. You will need to locate and successfully complete a Blue Sphere bonus stage in order to get a silver medal. Should you manage to collect all the rings on the bonus stage then you will be granted with a gold medal. We assume a mixture of silver and gold medals will unlock the Mean Bean mode so long as you manage to grab 20 medals.
Let us know if you've managed to unlock this coveted mode yet with a comment below.