How to add additional plots to a seaborn FacetGrid and specify colors

Is there a way to create a Seaborn line plot with all the lines gray and the mean as a red line? I'm trying to do this with relplot but I don't know how to separate the mean from the data (and it appears the mean isn't being plotted?).

Make reproducible data frame

np.random.seed(1)
n1 = 100
n2 = 10
idx = np.arange(0,n1*2)
x, y, cat, id2 = [], [], [], []

x1 = list(np.random.uniform(-10,10,n2))
for i in idx: 
    x.extend(x1)
    y.extend(list(np.random.normal(loc=0, scale=0.5, size=n2)))
    cat.extend(['A', 'B'][i > n1])
    id2.append(idx[i])

id2 = id2 * n2
id2.sort()
df1 = pd.DataFrame(list(zip(id2, x, y, cat)), 
                  columns =['id2', 'x', 'y', 'cat']
                 )

Plotting attempt

g = sns.relplot(
    data=df1, x='x', y='y', hue='id2',
    col='cat', kind='line',
    palette='Greys',
    facet_kws=dict(sharey=False, 
                   sharex=False
                  ),
    legend=False
)

I think you want units in the call to relplot and then add a layer of lineplot using map:

import seaborn as sns
import pandas as pd

fm = sns.load_dataset('fmri').query("event == 'stim'")
g = sns.relplot(
    data=fm, kind='line',
    col='region', x='timepoint', y='signal', units='subject',
    estimator=None, color='.7'
)
g.data = fm  # Hack needed to work around bug on v0.11, fixed in v0.12.dev
g.map(sns.lineplot, 'timepoint', 'signal', color='r', ci=None, lw=3)