  We introduce a new parking procedure called MVP parking in which $n$ cars
sequentially enter a one-way street with a preferred parking spot from the $n$
parking spots on the street. If their preferred spot is empty, they park there.
Otherwise, they park there and the car parked in that spot is bumped to the
next unoccupied spot on the street. If all cars can park under this parking
procedure, we say the list of preferences of the $n$ cars is an MVP parking
function of length $n$. We show that the set of (classical) parking functions
is exactly the set of MVP parking functions although the parking outcome (order
in which the cars park) is different under each parking process. Motivating the
question: Given a permutation describing the outcome of the MPV parking
process, what is the number of MVP parking functions resulting in that given
outcome? Our main result establishes a bound for this count which is tight
precisely when the permutation describing the parking outcome avoids the
patterns 321 and 3412. We then consider special cases of permutations and give
closed formulas for the number of MVP parking functions with those outcomes. In
particular, we show that the number of MVP parking functions which park in
reverse order (that is the permutation describing the outcome is the longest
word in $\mathfrak{S}_n$, which does not avoid the pattern 321) is given by the
$n$th Motzkin number. We also give families of permutations describing the
parking outcome for which the cardinality of the set of cars parking in that
order is exponential and others in which it is linear.
