The jaunt began in Canada on Wednesday night and moved into the US yesterday.
It will now continue to travel North America until the end of August, before heading across to Asia and Australasia in early 2020.
However there is still no word about a European leg – with fans in the continent, including the UK, still waiting for news.
After May shared a “mesmerising” photo of himself on the incredibly impressive set, fans were quick to post in the comments section that they want European dates added.
“I need this in Europe,” one said; while another wrote: “ahhhh i really hope you guys come to england, but i’m glad you’re enjoying the shows bri.”
“Amazing! European tour please,” wrote someone else, while another posted: “omg… pls come to europe.”
May’s own caption on the snap read: “Thanks good people of Tacoma ! That was an amazing night.
“Thanks to Ric Lipson for this photo – and for the wonderful work he and the Stufish team have put into this touring production.
MORE: ‘A few moments of panic’ as Queen tour launches
“And thanks to our brilliant crew for making it all happen tonight and every night.
“I love being suspended in space with my new pals – those amazing little planets !!! It’s mesmerising and inspiring.
“By the way, the piece I’ve played the last 2 nights while in space is part of Czech composer Dvorak’s New World Symphony. For me it’s a symbol. And I always loved this piece. Cheers all.”
May had said earlier this year that he expects Queen to visit the UK at some point – implying it could be for the final time.
“I’m hoping we will – [there’s been] no announcement,” he told BBC Radio 2.
“One more before we pop off, is my theory.”
The setlist is certainly impressive, and will leave no Queen fan disappointed – check it out here.
The Rhapsody Tour continues to San Jose tomorrow (Sunday).