Cook pasta in large pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain, reserving 1 cup pasta cooking liquid.
Meanwhile, melt 1/4 cup butter in large skillet over medium-high heat. Add squash and cook until almost tender, stirring often, about 6 minutes. Add mushrooms, sage, and remaining 1/4 cup butter; sauté until mushrooms are soft and squash is tender, about 8 minutes. Add spinach; stir until wilted, about 2 minutes. Stir in 1/2 cup cheese. Season with salt and pepper. Add pasta to sauce in skillet. Toss to coat, adding pasta cooking liquid by 1/4 cupfuls if dry. Sprinkle with 1/4 cup cheese.
