R multiple y axis interactive plot

I am trying to create a plot in R similar to this:

with up to 6 variables and it has to be reactive.

I tried plotly, however in plotly I would get axis ticks on the plot, and it gets messy, and I managed to get only one y axis out.

Is there a way to recreate the plot in plotly or any other interactive library?

My plotly code:

library(dplyr)
library(plotly)
library(tidyr)

data <- cbind(
  seq(from = 1, to = 30, by = 1),
  sample(seq(from = 100, to = 300, by = 10), size = 30, replace = TRUE),
  sample(seq(from = 1, to = 100, by = 9), size = 30, replace = TRUE),
  sample(seq(from = 50, to = 60, by = 2), size = 30, replace = TRUE),
  sample(seq(from = 100, to = 130, by = 1), size = 30, replace = TRUE)
) %>% 
  as.data.frame()

names(data) <- c("date", "a", "b", "x", "y")

plot_ly(x = ~data$date) %>%
  add_lines(y = ~data[, 2], name = "a", line = list(color = "red")) %>%
  add_lines(y = ~data[, 3], name = "b", line = list(color = "blue"), yaxis = "y2") %>%
  add_lines(y = ~data[, 4], name = "x", line = list(color = "green"), yaxis = "y3") %>%
  add_lines(y = ~data[, 5], name = "y", line = list(color = "pink"), yaxis = "y4") %>%
  layout(
    yaxis = list(
      side = "left",
      title = list("")
    ),
    yaxis2 = list(
      side = "left",
      overlaying = "y",
      anchor = "free"
    ),
    yaxis3 = list(
      side = "left",
      overlaying = "y",
      anchor = "free",
      position = 0.04
    ),
    yaxis4 = list(
      side = "left",
      overlaying = "y",
      anchor = "free",
      position = 0.08
    ),
    margin = list(pad = 30)
  )

With the highcharter package one can generate nice time series plots with multiple y-axes:

library(highcharter)

set.seed(1)
n <- 100
x1 <- cumsum(rnorm(n))
x2 <- cumsum(runif(n)-0.5)+10
x3 <- cumsum(rnorm(n,0,20))+100
x4 <- cumsum(rnorm(n,0,20))+1000

highchart() %>% 
  hc_add_series(data = x1) %>% 
  hc_add_series(data = x2, yAxis = 1) %>% 
  hc_add_series(data = x3, yAxis = 2) %>%
  hc_add_series(data = x4, yAxis = 3) %>%
   hc_yAxis_multiples(
     list(lineWidth = 3, lineColor='#7cb5ec', title=list(text="First y-axis")),
     list(lineWidth = 3, lineColor="#434348", title=list(text="Second y-axis")),
     list(lineWidth = 3, lineColor="#90ed7d", title=list(text="Third y-axis")),
     list(lineWidth = 3, lineColor="#f7a35c", title=list(text="Fourth y-axis"))
   )