Mixed models with mlogit in R - Random intercepts?

Question

I want to fit a very simple mixed-effects model, with a couple of fixed effects and random intercepts (no random slopes), using the mlogit package in R. My categorical outcome variable has three levels, so I cannot use the lme4 package.

However, I keep googling and stack-ing and CRAN-ing (?) about this, but nowhere am I able to find a good solution. Any help out there on how to do this with the mlogit package? -- Or are there any similar alternatives in other R packages (or in SPSS, Stata or Minitab, or via packages in Python/Julia)?

See code below for my data structure and what type of model I would like to fit (I know how to fit a fixed-effects only model with mlogit (cf. fixed_model below); I just want to add random intercepts):

library(mlogit)
library(dfidx)

# Make variables: 
Outcome = c("y","z","y","z","x","z","y","x","x","x","z",
"y","z","x","x","y","z","x", "x", "y")
Predictor = rep(c("M", "F"), 10)
RandomIntercept = rep(c("A", "B", "C", "D"), 5)

# Make data frame
df <- data.frame(Outcome, Predictor, RandomIntercept) 

# Make mlogit-ready dataframe:
df_mlogit <- dfidx(df, choice = "Outcome", shape = "wide", id.var = "RandomIntercept")

# Display first observations: 
head(df_mlogit)

# Make fixed-effect-only model: 
fixed_model <- mlogit::mlogit(Outcome ~ 1 | Predictor, data = df_mlogit, reflevel = "x")

#Display results: 
fixed_model

# The kind of model I want, in lme4-syntax: 
dream_model <- lme4::glmer(Outcome ~ Predictor + (1|RandomIntercept), family = "binomial")