The proposal calls for a three-story addition with at least 20 classrooms or other educational spaces. It could cost about $25 million to build.
Stevenson has 833,000 square feet of space now, but school officials say more classrooms are needed to accommodate growing enrollment.
More than 4,100 students attend Stevenson this term. Enrollment could hit 4,500 by 2025, officials have said.
Lincolnshire officials will review the plan during a committee of the whole meeting following the village board's 7 p.m. session at village hall, 1 Olde Half Day Road.
Village staff subsequently will examine the site, engineering, lighting and landscape plans for the project, among other elements. Public hearings and additional discussions will be held before the village board decides if the project should be greenlit.
Stevenson High spokesman Jim Conrey said he doesn't expect any "major turbulence on the way to approval."
"Our relationship with the village is good, and we hope they'll agree with us that the addition is not only a good idea, but a necessary one," Conrey said.
Lincolnshire Trustee Karen Feldman's children attend Stevenson, and she said she knows the school needs more space. But she also realizes an expansion will affect traffic and other aspects of life in Lincolnshire, so she's glad to have the chance to review the project first.
"Our job is to put the community first," Feldman said.
If the project gets the green light, construction could begin this fall and be completed in summer 2019.