diff --git a/internal/token.go b/internal/token.go
index b417456..8389f24 100644
--- a/internal/token.go
+++ b/internal/token.go
@@ -105,14 +105,6 @@
 	return nil
 }
 
-// RegisterBrokenAuthHeaderProvider previously did something. It is now a no-op.
-//
-// Deprecated: this function no longer does anything. Caller code that
-// wants to avoid potential extra HTTP requests made during
-// auto-probing of the provider's auth style should set
-// Endpoint.AuthStyle.
-func RegisterBrokenAuthHeaderProvider(tokenURL string) {}
-
 // AuthStyle is a copy of the golang.org/x/oauth2 package's AuthStyle type.
 type AuthStyle int
 
@@ -149,6 +141,11 @@
 	return c
 }
 
+type authStyleCacheKey struct {
+	url      string
+	clientID string
+}
+
 // AuthStyleCache is the set of tokenURLs we've successfully used via
 // RetrieveToken and which style auth we ended up using.
 // It's called a cache, but it doesn't (yet?) shrink. It's expected that
@@ -156,26 +153,26 @@
 // small.
 type AuthStyleCache struct {
 	mu sync.Mutex
-	m  map[string]AuthStyle // keyed by tokenURL
+	m  map[authStyleCacheKey]AuthStyle
 }
 
 // lookupAuthStyle reports which auth style we last used with tokenURL
 // when calling RetrieveToken and whether we have ever done so.
-func (c *AuthStyleCache) lookupAuthStyle(tokenURL string) (style AuthStyle, ok bool) {
+func (c *AuthStyleCache) lookupAuthStyle(tokenURL, clientID string) (style AuthStyle, ok bool) {
 	c.mu.Lock()
 	defer c.mu.Unlock()
-	style, ok = c.m[tokenURL]
+	style, ok = c.m[authStyleCacheKey{tokenURL, clientID}]
 	return
 }
 
 // setAuthStyle adds an entry to authStyleCache, documented above.
-func (c *AuthStyleCache) setAuthStyle(tokenURL string, v AuthStyle) {
+func (c *AuthStyleCache) setAuthStyle(tokenURL, clientID string, v AuthStyle) {
 	c.mu.Lock()
 	defer c.mu.Unlock()
 	if c.m == nil {
-		c.m = make(map[string]AuthStyle)
+		c.m = make(map[authStyleCacheKey]AuthStyle)
 	}
-	c.m[tokenURL] = v
+	c.m[authStyleCacheKey{tokenURL, clientID}] = v
 }
 
 // newTokenRequest returns a new *http.Request to retrieve a new token
@@ -218,7 +215,7 @@
 func RetrieveToken(ctx context.Context, clientID, clientSecret, tokenURL string, v url.Values, authStyle AuthStyle, styleCache *AuthStyleCache) (*Token, error) {
 	needsAuthStyleProbe := authStyle == AuthStyleUnknown
 	if needsAuthStyleProbe {
-		if style, ok := styleCache.lookupAuthStyle(tokenURL); ok {
+		if style, ok := styleCache.lookupAuthStyle(tokenURL, clientID); ok {
 			authStyle = style
 			needsAuthStyleProbe = false
 		} else {
@@ -248,7 +245,7 @@
 		token, err = doTokenRoundTrip(ctx, req)
 	}
 	if needsAuthStyleProbe && err == nil {
-		styleCache.setAuthStyle(tokenURL, authStyle)
+		styleCache.setAuthStyle(tokenURL, clientID, authStyle)
 	}
 	// Don't overwrite `RefreshToken` with an empty value
 	// if this was a token refreshing request.
diff --git a/internal/token_test.go b/internal/token_test.go
index c08862a..ef28c11 100644
--- a/internal/token_test.go
+++ b/internal/token_test.go
@@ -75,3 +75,48 @@
 		t.Errorf("expiration time = %v; want %v", e, want)
 	}
 }
+
+func TestAuthStyleCache(t *testing.T) {
+	var c LazyAuthStyleCache
+
+	cases := []struct {
+		url      string
+		clientID string
+		style    AuthStyle
+	}{
+		{
+			"https://host1.example.com/token",
+			"client_1",
+			AuthStyleInHeader,
+		}, {
+			"https://host2.example.com/token",
+			"client_2",
+			AuthStyleInParams,
+		}, {
+			"https://host1.example.com/token",
+			"client_3",
+			AuthStyleInParams,
+		},
+	}
+
+	for _, tt := range cases {
+		t.Run(tt.clientID, func(t *testing.T) {
+			cc := c.Get()
+			got, ok := cc.lookupAuthStyle(tt.url, tt.clientID)
+			if ok {
+				t.Fatalf("unexpected auth style found on first request: %v", got)
+			}
+
+			cc.setAuthStyle(tt.url, tt.clientID, tt.style)
+
+			got, ok = cc.lookupAuthStyle(tt.url, tt.clientID)
+			if !ok {
+				t.Fatalf("auth style not found in cache")
+			}
+
+			if got != tt.style {
+				t.Fatalf("auth style mismatch, got=%v, want=%v", got, tt.style)
+			}
+		})
+	}
+}