Honestly speaking, Monster is such a very unique anime in its own way that it's hard to name something similar to it. I'd like to think that Death Note has some similarities to it in the way it has thriller elements in it and involves stuff like crime investigation, though it's a lot more fast paced than the realistic slow + haunting pave that Monster has. I'd like to assume that you've already watched Death Note cuz it's so popular and mainstream, henceforth I'd recommend another one that has some similarities, which is Psycho-Pass. This one also has thriller elements involving the aspects of crime & society integrally, though it's more fast paced like Death Note than being serene & deliberate paced like Monster is, plus it also involves a ton of cyberpunk elements as well.
OT: Haven't watched Kaleido Star, but that OP is good & catchy, 8/10