Tennessee Republican Gov. Bill Lee plans this week to propose placing armed guards at every school in his state, and he indicated that he is open to some gun reform measures in the wake of the shooting at a private Christian school in Nashville that left six dead.

While it still needs legislative approval, Lee’s plan would expand a proposal to station armed guards at all public schools in Tennessee and give grant funding to allow private schools to also hire armed guards, The Tennessean reported Friday. The state cannot require private schools to hire armed guards, but it can require the guards hired by private schools to have the same level of training as those in public schools.

That means the new plan could apply to Covenant School, a private Presbyterian school where 28-year-old Audrey Hale killed three nine-year-olds and three staffers in their 60s last week.