How to customize toolbar in Bottomsheet layout?

I'm using a CollapsingToolbarLayout within a CoordinatorLayout for my bottomsheet's layout. The layout looks like this -

<android.support.design.widget.CoordinatorLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    android:id="@+id/bottomSheet"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:background="@color/darkBackgroundMainTranslucent"
    app:behavior_hideable="true"
    app:layout_behavior="@string/bottom_sheet_behavior">

    <android.support.design.widget.AppBarLayout
        android:id="@+id/appbar"
        android:layout_width="match_parent"
        android:layout_height="@dimen/detail_backdrop_height"
        android:theme="@style/ThemeOverlay.AppCompat.Dark.ActionBar"
        android:fitsSystemWindows="true">

        <android.support.design.widget.CollapsingToolbarLayout
            android:id="@+id/collapsing_toolbar"
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            app:layout_scrollFlags="scroll|exitUntilCollapsed"
            android:fitsSystemWindows="true"
            app:contentScrim="@color/colorScrim"
            app:expandedTitleMarginStart="48dp"
            app:expandedTitleMarginEnd="64dp">

            <ImageView
                android:id="@+id/backdrop"
                android:layout_width="match_parent"
                android:layout_height="match_parent"
                android:scaleType="centerCrop"
                android:fitsSystemWindows="true"
                android:contentDescription="@string/poster_string"
                app:layout_collapseMode="parallax" />

            <android.support.v7.widget.Toolbar
                android:id="@+id/bottomsheet_toolbar"
                android:layout_width="match_parent"
                android:layout_height="?attr/actionBarSize"
                app:popupTheme="@style/AppTheme.PopupOverlay"
                app:layout_collapseMode="pin" />

        </android.support.design.widget.CollapsingToolbarLayout>

    </android.support.design.widget.AppBarLayout>

    <android.support.v4.widget.NestedScrollView
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        app:layout_behavior="@string/appbar_scrolling_view_behavior"
        android:id="@+id/nestedScrollView">

        <LinearLayout
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:orientation="vertical"
            android:paddingTop="24dp">

            <android.support.v7.widget.CardView
                android:layout_width="match_parent"
                android:layout_height="wrap_content"
                android:layout_margin="@dimen/card_margin">

                <LinearLayout
                    style="@style/Widget.CardContent"
                    android:layout_width="match_parent"
                    android:layout_height="wrap_content">

                    <TextView
                        android:layout_width="match_parent"
                        android:layout_height="wrap_content"
                        android:text="Title"
                        android:textAppearance="@style/TextAppearance.AppCompat.Title" />

                    <TextView
                        android:id="@+id/bottomsheet_title"
                        android:layout_width="match_parent"
                        android:layout_height="wrap_content"
                        android:textIsSelectable="true"/>

                </LinearLayout>

            </android.support.v7.widget.CardView>


        </LinearLayout>

    </android.support.v4.widget.NestedScrollView>

</android.support.design.widget.CoordinatorLayout>

I was wondering whether it would be possible to customize the toolbar inside the CollapsingToolbarLayout to add an up button and set its title without setting that toolbar as the supportactionbar.