extract coefficients from more than one linear regression model with multiple terms in r

I am trying to generate a data frame of intercepts and coefficients for multiple different linear regression models generated from subsets of a data set. I cannot share my data unfortunately but I can explain it using the mtcars set. I am creating a regression model predicting mpg from cyl, hp, and wt for each value of carb.After digging around for a while, I found many examples that do what I want but only for a model with 1 predictor (like mpg~wt). It all falls apart when I add the other terms. This is what I have based my work so far on:https://community.rstudio.com/t/extract-slopes-by-group-broom-dplyr/2751/8Efficient way to extract coefficients from many linear regression lines

This is what I have tried

library(tidyverse);library(broom)df <- mtcarstryme <- df %>%  split(.$carb)%>%  map(~lm(mpg~cyl+hp+wt,data=.x)) %>%  map_df(tidy)

with this result

    term            estimate    std.error   statistic   p.value1   (Intercept) 46.034633   7.68430306  5.99073626  9.31E-032   cyl         2.650503624 4.14371413  0.63964442  5.68E-013   hp          -0.230007961    0.1573354   -1.46189576 2.40E-014   wt          -5.231999683    9.23136027  -0.56676368 6.11E-015   (Intercept) 39.84451509 2.95537984  13.48202845 1.03E-056   cyl         -0.846094229    0.93995084  -0.90014732 4.03E-017   hp          -0.007452737    0.03998485  -0.18638901 8.58E-018   wt          -4.133340298    1.42757472  -2.89535829 2.75E-029   (Intercept) 17.50267062 22.13706712 0.79064993  5.74E-0110  cyl         NA          NA          NA          NA11  hp          NA          NA          NA          NA12  wt          -0.3115727  5.73067255  -0.05436931 9.65E-0113  (Intercept) 45.33390978 12.93999647 3.50339429  1.28E-0214  cyl         -4.195214198    3.492613    -1.20116778 2.75E-0115  hp          0.029361878 0.04927895  0.59583008  5.73E-0116  wt          -1.239041102    1.03937377  -1.19210349 2.78E-0117  (Intercept) 19.7            NaN         NaN         NaN18  cyl         NA          NA          NA          NA19  hp          NA          NA          NA          NA20  wt          NA          NA          NA          NA21  (Intercept) 15          NaN         NaN         NaN22  cyl         NA          NA          NA          NA23  hp          NA          NA          NA          NA24  wt          NA          NA          NA          NA

what I want is a table that looks like this:

carb    intercept   cyl         hp          wt1   46.034633   2.650503624 -0.230007961    -5.2319996832   39.84451509 -0.846094229    -0.007452737    -4.1333402983   17.50267062 NA          NA          -0.31157274   45.33390978 -4.195214198    0.029361878 -1.2390411026   19.7            NA          NA          NA8   15          NA          NA          NA

I don't know how to bring the value of the grouping variable in. If I can get that added to what I already have I know how to transpose the data into the form I need.

I am updating a bit, as an answer here gave me what I wanted, but is causing an error that I can't seem to fix. the solution uses lmList from the nlme library. The code I am using is this

fit <- lmList(SentLength~Unified_UPPER+Unified_LOWER+GRADE | SentType, data=df, na.omit)

and this is the data I am running it on:SentType    SentLength  Unified_UPPER   Unified_LOWER   GRADEJail        0.06578947  0.06666667      0.06666667      3Other       0           6               0               4Other       0           6               6               1Probation   6           0               0               1Other       0           9               0               6Jail        1.41447368  6               0               3Probation   6           0               0               1Probation   6           0               0               1Probation   12          0               0               2Jail        6           16              6               6Prison      36          27              21              5Probation   24          9               0               6Jail        0.23026316  0.5             0               1Jail        0.09868421  0.06666667      0.06666667      1Probation   60          27              21              6Probation   6           1               0               1Probation   24          0               0               3Prison      36          54              36              8Probation   24          9               0               6Probation   6           0               0               1Probation   0           0.06666667      0.06666667      1Probation   24          0               0               3Jail        0.13157895  1               0.06666667      1Jail        0.09868421  1               0.1             1Prison      42          60              48              8Probation   6           0               0               2Other       0           0               0               1Prison      6           6               6               1Prison      6           6               6               1Other       0           16              9               7

I get this error:Error in na.fail.default(data) : missing values in objectdespite no missing values in the data. Can anyone help with this?