There are a bunch of soteriological stances out there that try to either combine Calvinism and Arminianism or find middle ground between the two. Some of them, such as Amyraldism (sometimes known as Four-Point Calvinism) tend to lean towards universalism (which we’ll talk about tomorrow). However, one that is gaining considerable momentum in evangelical circles is “New Calvinism” or modified Calvinism, the soteriology supported by pastors Mark Driscoll, Al Mohler, CJ Mahaney, and Tim Keller.
In its most basic terms, this “-ism” says that God has certain people that he picks and His will is not to be thwarted (Moses, Paul, etc). However, at the same time, God reaches His hand out to everyone else on the planet and they are allowed to choose to come to Him or not. Examples of this may be represented in Biblical figures such as the unclean woman (Mark 5:25-34), the Centurion (Matthew 8:5-13), or the Ethiopian eunuch (Acts 8:26-39) who were not directly called by name to be followers of Christ (unlike many of the other characters of the Bible) but seemingly chose to follow Him. The “elect” simply means all who are in Christ, not just those handpicked by God.
Support: “Christ died for the purpose of securing the sure and certain salvation of His own, His elect... Christ died for all people... If five-point Calvinism is right and no payment has been made for the non-elect, then how can God genuinely love the world and desire the salvation of all people? There is a genuine open door for salvation for anyone who believes in Jesus, and this makes the rejection of Jesus completely inexcusable.” (Doctrine, Driscoll, p 270)
Opposition: Those opposed to Arminianism will still say the “two-handed” side of this suggests a works based salvation. Calvinists will say even those who chose to take the hand offered were predestined to do so; that God in His infinite wisdom knew who would take His hand and so only offered it to those people.