You can collect several 1-Up Mushrooms on Spaceship Mario. As you collect stars, the following 1-Up options will appear on Spaceship Mario.

Grab Yoshi off of the "nose" and use the star pegs to swing up to a hidden island with 10 fruit. Eat them all for a 1-Up.

Grab a Cloud Flower and make platforms to reach a 1-Up on a cloud high above.

Spin into the random item block for a chance at a 1-Up.

Near Mario's left ear (your right) is a warp pipe that takes you to a 1-Up minigame. Feed the Luma to spin a number of random item blocks for a chance to win 1-Ups.

Talk to the Gearmo Robots when they show up on the planet to receive 1-Ups.