Illinois State Senator Rachel Ventura (D-Joliet) has introduced SB 2158, which would establish a top-two system. It even extends the top-two system to presidential elections. Here is the text. See page 45 of the bill, in which section 7-60 would say, “Not withstanding any other provision of law, the two candidates in any primary election who receive the most votes in the primary election, regardless of the party affiliation of the candidates, shall be the only two candidates certified to participate in the general election.”
All Illinois primaries for federal and state office are in early March, so this bill, if enacted, would require anyone who wanted to run in November to file in late November of the odd year before the election year.
Ordinarily, supporters of top-two never write their bills or initiative to include presidential elections, because if they did, the major party presidential nominees wouldn’t be the same in each state. For example, in 2016, the Illinois presidential primary totals for the top three candidates were: Hillary Clinton 1,039,555; Bernie Sanders 999,494; Donald Trump 562,464. Under the terms of SB 2158, the only presidential candidates who would be on the November ballot in Illinois would have been Clinton and Sanders.