Q:

R Mapply function over list of tibbles, where each tibble loop over variables in second dataframe

I have a function similar to a regression, that I want to run using each tibble in list x to predcit each variable in tibble y (i.e., not a list). I'm using the format:
mapply(FUN, x, y, SIMPLIFY= TRUE) 
However, if x include a list of two tibbles (Tibble1 and Tibble2); and y include two variables (V1 and V2); I would like to have 4 different outputs but I only get 2.
That is, I want the Tibble1 data to produce two separate outcomes, one for V1 and one for V2 and then Tibble2 two produce separate outcomes for V1 and V2. 
Does this make sense? 

A:

I had difficulties to get @akrun's answer to work; but based on the comment by @Onyambu, I finally solved my problem which I hope can help others: 
# Get variable names in list y
variables <- dput(names(y))
# Duplicate variables names in y to as many different objects in list x
variables <- rep(variables, length(x))
# Create dataframe with duplicated variables
y <- y[c(variables)]
# Order columns alphabetically
y <- y[,order(colnames(y))]

output <- mapply(myFUN, x, y, SIMPLIFY=FALSE)

