diff --git a/doc/users/next_whats_new/2020-02-24-mathtext-fallback.rst b/doc/users/next_whats_new/2020-02-24-mathtext-fallback.rst
@@ -0,0 +1,5 @@
+Add generalized "mathtext.fallback" rcParam
+------------------------------------------------------------------------
+New  "mathtext.fallback" rcParam. Takes "cm", "stix", "stixsans"
+or "none" to turn fallback off. "mathtext.fallback_to_cm" is
+deprecated, but if used, will override new fallback.
diff --git a/lib/matplotlib/__init__.py b/lib/matplotlib/__init__.py
@@ -602,6 +602,7 @@ def gen_candidates():
 _deprecated_remain_as_none = {
     'animation.avconv_path': ('3.3',),
     'animation.avconv_args': ('3.3',),
+    'mathtext.fallback_to_cm': ('3.3',),
     'keymap.all_axes': ('3.3',),
 }
 

diff --git a/lib/matplotlib/mathtext.py b/lib/matplotlib/mathtext.py
@@ -769,10 +769,17 @@ class UnicodeFonts(TruetypeFonts):
 
     def __init__(self, *args, **kwargs):
         # This must come first so the backend's owner is set correctly
-        if rcParams['mathtext.fallback_to_cm']:
-            self.cm_fallback = BakomaFonts(*args, **kwargs)
-        else:
-            self.cm_fallback = None
+        fallback_rc = rcParams['mathtext.fallback']
+        if rcParams['mathtext.fallback_to_cm'] is not None:
+            fallback_rc = ('cm' if rcParams['mathtext.fallback_to_cm']
+                           else None)
+
+        font_class = {'stix': StixFonts,
+                      'stixsans': StixSansFonts,
+                      'cm': BakomaFonts
+                      }.get(fallback_rc)
+        self.cm_fallback = font_class(*args, **kwargs) if font_class else None
+
         TruetypeFonts.__init__(self, *args, **kwargs)
         self.fontmap = {}
         for texfont in "cal rm tt it bf sf".split():
@@ -783,6 +790,21 @@ def __init__(self, *args, **kwargs):
         font = findfont(prop)
         self.fontmap['ex'] = font
 
+        # include STIX sized alternatives for glyphs if fallback is STIX
+        if isinstance(self.cm_fallback, StixFonts):
+            stixsizedaltfonts = {
+                 0: 'STIXGeneral',
+                 1: 'STIXSizeOneSym',
+                 2: 'STIXSizeTwoSym',
+                 3: 'STIXSizeThreeSym',
+                 4: 'STIXSizeFourSym',
+                 5: 'STIXSizeFiveSym'}
+
+            for size, name in stixsizedaltfonts.items():
+                fullpath = findfont(name)
+                self.fontmap[size] = fullpath
+                self.fontmap[name] = fullpath
+
     _slanted_symbols = set(r"\int \oint".split())
 
     def _map_virtual_font(self, fontname, font_class, uniindex):
@@ -830,16 +852,19 @@ def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
 
         if not found_symbol:
             if self.cm_fallback:
-                if isinstance(self.cm_fallback, BakomaFonts):
-                    _log.warning(
-                        "Substituting with a symbol from Computer Modern.")
-                if (fontname in ('it', 'regular') and
-                        isinstance(self.cm_fallback, StixFonts)):
-                    return self.cm_fallback._get_glyph(
-                            'rm', font_class, sym, fontsize)
-                else:
-                    return self.cm_fallback._get_glyph(
-                        fontname, font_class, sym, fontsize)
+                if (fontname in ('it', 'regular')
+                        and isinstance(self.cm_fallback, StixFonts)):
+                    fontname = 'rm'
+
+                g = self.cm_fallback._get_glyph(fontname, font_class,
+                                                sym, fontsize)
+                fname = g[0].family_name
+                if fname in list(BakomaFonts._fontmap.values()):
+                    fname = "Computer Modern"
+                _log.warning("Substituting symbol {} "
+                             "from {}".format(sym, fname))
+                return g
+
             else:
                 if (fontname in ('it', 'regular')
                         and isinstance(self, StixFonts)):

diff --git a/lib/matplotlib/mpl-data/stylelib/classic.mplstyle b/lib/matplotlib/mpl-data/stylelib/classic.mplstyle
@@ -154,9 +154,10 @@ mathtext.bf  : serif:bold
 mathtext.sf  : sans\-serif
 mathtext.fontset : cm # Should be 'cm' (Computer Modern), 'stix',
                       # 'stixsans' or 'custom'
-mathtext.fallback_to_cm : True  # When True, use symbols from the Computer Modern
-                                # fonts when a symbol can not be found in one of
-                                # the custom math fonts.
+mathtext.fallback: cm  # Select fallback font from ['cm' (Computer Modern), 'stix'
+                       # 'stixsans'] when a symbol can not be found in one of the 
+                       # custom math fonts. Select 'None' to not perform fallback
+                       # and replace the missing character by a dummy.
 
 mathtext.default : it # The default font to use for math.
                       # Can be any of the LaTeX font names, including

diff --git a/lib/matplotlib/rcsetup.py b/lib/matplotlib/rcsetup.py
@@ -413,6 +413,37 @@ def validate_font_properties(s):
     return s
 
 
+def _validate_mathtext_fallback_to_cm(b):
+    """
+    Temporary validate for fallback_to_cm, while deprecated
+
+    """
+    if isinstance(b, str):
+        b = b.lower()
+    if b is None or b == 'none':
+        return None
+    else:
+        cbook.warn_deprecated(
+            "3.3", message="Support for setting the 'mathtext.fallback_to_cm' rcParam "
+            "is deprecated since %(since)s and will be removed "
+            "%(removal)s; use 'mathtext.fallback : 'cm' instead.")
+        return validate_bool_maybe_none(b)
+
+
+def _validate_mathtext_fallback(s):
+    _fallback_fonts = ['cm', 'stix', 'stixsans']
+    if isinstance(s, str):
+        s = s.lower()
+    if s is None or s == 'none':
+        return None
+    elif s.lower() in _fallback_fonts:
+        return s
+    else:
+        raise ValueError(f"{s} is not a valid fallback font name. Valid fallback "
+                         f"font names are {','.join(_fallback_fonts)}. Passing "
+                         f"'None' will turn fallback off.")
+
+
 validate_fontset = ValidateInStrings(
     'fontset',
     ['dejavusans', 'dejavuserif', 'cm', 'stix', 'stixsans', 'custom'],
@@ -1150,7 +1181,8 @@ def _convert_validator_spec(key, conv):
     'mathtext.default':        [
         'it',
         ['rm', 'cal', 'it', 'tt', 'sf', 'bf', 'default', 'bb', 'frak', 'scr', 'regular']],
-    'mathtext.fallback_to_cm': [True, validate_bool],
+    'mathtext.fallback_to_cm': [None, _validate_mathtext_fallback_to_cm],
+    'mathtext.fallback':       ['cm', _validate_mathtext_fallback],
 
     'image.aspect':        ['equal', validate_aspect],  # equal, auto, a number
     'image.interpolation': ['antialiased', validate_string],

diff --git a/lib/matplotlib/tests/test_mathtext.py b/lib/matplotlib/tests/test_mathtext.py
@@ -1,4 +1,5 @@
 import io
+import os
 import re
 
 import numpy as np
@@ -283,3 +284,48 @@ def test_single_minus_sign():
 def test_spaces(fig_test, fig_ref):
     fig_test.subplots().set_title(r"$1\,2\>3\ 4$")
     fig_ref.subplots().set_title(r"$1\/2\:3~4$")
+
+
+def test_mathtext_fallback_valid():
+    for fallback in ['cm', 'stix', 'stixsans', 'None']:
+        mpl.rcParams['mathtext.fallback'] = fallback
+
+
+@pytest.mark.xfail
+def test_mathtext_fallback_invalid():
+    for fallback in ['abc', '']:
+        mpl.rcParams['mathtext.fallback'] = fallback
+
+
+@pytest.mark.xfail
+def test_mathtext_fallback_to_cm_invalid():
+    for fallback in [True, False]:
+        mpl.rcParams['mathtext.fallback_to_cm'] = fallback
+
+
+@pytest.mark.parametrize(
+    "fallback,fontlist",
+    [("cm", ['DejaVu Sans', 'mpltest', 'STIXGeneral', 'cmr10', 'STIXGeneral']),
+     ("stix", ['DejaVu Sans', 'mpltest', 'STIXGeneral'])])
+def test_mathtext_fallback(fallback, fontlist):
+    mpl.font_manager.fontManager.addfont(
+        os.path.join((os.path.dirname(os.path.realpath(__file__))), 'mpltest.ttf'))
+    mpl.rcParams["svg.fonttype"] = 'none'
+    mpl.rcParams['mathtext.fontset'] = 'custom'
+    mpl.rcParams['mathtext.rm'] = 'mpltest'
+    mpl.rcParams['mathtext.it'] = 'mpltest:italic'
+    mpl.rcParams['mathtext.bf'] = 'mpltest:bold'
+    mpl.rcParams['mathtext.fallback'] = fallback
+
+    test_str = r'a$A\AA\breve\gimel$'
+
+    buff = io.BytesIO()
+    fig, ax = plt.subplots()
+    fig.text(.5, .5, test_str, fontsize=40, ha='center')
+    fig.savefig(buff, format="svg")
+    char_fonts = [
+        line.split("font-family:")[-1].split(";")[0]
+        for line in str(buff.getvalue()).split(r"\n") if "tspan" in line
+    ]
+    assert char_fonts == fontlist
+    mpl.font_manager.fontManager.ttflist = mpl.font_manager.fontManager.ttflist[:-1]
diff --git a/matplotlibrc.template b/matplotlibrc.template
@@ -329,9 +329,10 @@
 #mathtext.rm:  sans
 #mathtext.sf:  sans
 #mathtext.tt:  monospace
-#mathtext.fallback_to_cm: True  # When True, use symbols from the Computer Modern
-                                # fonts when a symbol can not be found in one of
-                                # the custom math fonts.
+#mathtext.fallback: cm  # Select fallback font from ['cm' (Computer Modern), 'stix'
+                        # 'stixsans'] when a symbol can not be found in one of the 
+                        # custom math fonts. Select 'None' to not perform fallback
+                        # and replace the missing character by a dummy symbol.
 #mathtext.default: it  # The default font to use for math.
                        # Can be any of the LaTeX font names, including
                        # the special name "regular" for the same font

diff --git a/tutorials/text/mathtext.py b/tutorials/text/mathtext.py
@@ -296,8 +296,9 @@
 The fonts used should have a Unicode mapping in order to find any
 non-Latin characters, such as Greek.  If you want to use a math symbol
 that is not contained in your custom fonts, you can set
-:rc:`mathtext.fallback_to_cm` to ``True`` which will cause the mathtext system
-to use characters from the default Computer Modern fonts whenever a particular
+:rc:`mathtext.fallback` to either ``'cm'``, ``'stix'`` or ``'stixsans'``
+which will cause the mathtext system to use
+characters from an alternative font whenever a particular
 character can not be found in the custom font.
 
 Note that the math glyphs specified in Unicode have evolved over time, and many