diff --git a/connection.go b/connection.go
index ebb86b73..21ee46f7 100644
--- a/connection.go
+++ b/connection.go
@@ -174,13 +174,17 @@ func (c *Connection) Init() error {
 	initOp.MaxReadahead = maxReadahead
 	initOp.MaxWrite = buffer.MaxWriteSize
 
-	initOp.Flags = 0
+	initOp.OutFlags = 0
+	initOp.OutFlags2 = 0
+
+	// Initialize the extended flags
+	initOp.OutFlags |= fusekernel.InitExt
 
 	// Tell the kernel not to use pitifully small 4 KiB writes.
-	initOp.Flags |= fusekernel.InitBigWrites
+	initOp.OutFlags |= fusekernel.InitBigWrites
 
 	if c.cfg.EnableAsyncReads {
-		initOp.Flags |= fusekernel.InitAsyncRead
+		initOp.OutFlags |= fusekernel.InitAsyncRead
 	}
 
 	// kernel 4.20 increases the max from 32 -> 256
@@ -189,46 +193,51 @@ func (c *Connection) Init() error {
 
 	// Enable writeback caching if the user hasn't asked us not to.
 	if !c.cfg.DisableWritebackCaching {
-		initOp.Flags |= fusekernel.InitWritebackCache
+		initOp.OutFlags |= fusekernel.InitWritebackCache
 	}
 
 	// Enable caching symlink targets in the kernel page cache if the user opted
 	// into it (might require fixing the size field of inode attributes first):
 	if c.cfg.EnableSymlinkCaching && cacheSymlinks {
-		initOp.Flags |= fusekernel.InitCacheSymlinks
+		initOp.OutFlags |= fusekernel.InitCacheSymlinks
 	}
 
 	// Tell the kernel to treat returning -ENOSYS on OpenFile as not needing
 	// OpenFile calls at all (Linux >= 3.16):
 	if c.cfg.EnableNoOpenSupport && noOpenSupport {
-		initOp.Flags |= fusekernel.InitNoOpenSupport
+		initOp.OutFlags |= fusekernel.InitNoOpenSupport
 	}
 
 	// Tell the kernel to treat returning -ENOSYS on OpenDir as not needing
 	// OpenDir calls at all (Linux >= 5.1):
 	if c.cfg.EnableNoOpendirSupport && noOpendirSupport {
-		initOp.Flags |= fusekernel.InitNoOpendirSupport
+		initOp.OutFlags |= fusekernel.InitNoOpendirSupport
 	}
 
 	// Tell the Kernel to allow sending parallel lookup and readdir operations.
 	if c.cfg.EnableParallelDirOps {
-		initOp.Flags |= fusekernel.InitParallelDirOps
+		initOp.OutFlags |= fusekernel.InitParallelDirOps
 	}
 
 	if c.cfg.EnableAtomicTrunc {
-		initOp.Flags |= fusekernel.InitAtomicTrunc
+		initOp.OutFlags |= fusekernel.InitAtomicTrunc
 	}
 
 	if c.cfg.EnableReaddirplus {
 		// Enable Readdirplus support, allowing the kernel to use Readdirplus
-		initOp.Flags |= fusekernel.InitDoReaddirplus
+		initOp.OutFlags |= fusekernel.InitDoReaddirplus
 
 		if c.cfg.EnableAutoReaddirplus {
 			// Enable adaptive Readdirplus, allowing the kernel to choose between Readdirplus and Readdir
-			initOp.Flags |= fusekernel.InitReaddirplusAuto
+			initOp.OutFlags |= fusekernel.InitReaddirplusAuto
 		}
 	}
 
+	// Tell the kernel to allow shared mmap() for files opened with OpenDirectIO
+	if c.cfg.AllowDirectIOMmap {
+		initOp.OutFlags2 |= fusekernel.InitDirectIOAllowMmap
+	}
+
 	return c.Reply(ctx, nil)
 }
 
diff --git a/internal/fusekernel/fuse_kernel.go b/internal/fusekernel/fuse_kernel.go
index 8c47b524..fa1d9c95 100644
--- a/internal/fusekernel/fuse_kernel.go
+++ b/internal/fusekernel/fuse_kernel.go
@@ -252,7 +252,8 @@ var openResponseFlagNames = []flagName{
 }
 
 // The InitFlags are used in the Init exchange.
-type InitFlags uint32
+type InitFlags uint32  // first 32 bit flags
+type InitFlags2 uint32 // second 32-bit flags, used when InitExt is set in the first 32 bits
 
 const (
 	InitAsyncRead        InitFlags = 1 << 0
@@ -277,10 +278,13 @@ const (
 	InitMaxPages         InitFlags = 1 << 22
 	InitCacheSymlinks    InitFlags = 1 << 23
 	InitNoOpendirSupport InitFlags = 1 << 24
+	InitExt              InitFlags = 1 << 30
 
 	InitCaseSensitive InitFlags = 1 << 29 // OS X only
 	InitVolRename     InitFlags = 1 << 30 // OS X only
 	InitXtimes        InitFlags = 1 << 31 // OS X only
+
+	InitDirectIOAllowMmap InitFlags2 = 1 << 4
 )
 
 type flagName struct {
@@ -738,6 +742,7 @@ type InitIn struct {
 	Minor        uint32
 	MaxReadahead uint32
 	Flags        uint32
+	Flags2       uint32
 }
 
 const InitInSize = int(unsafe.Sizeof(InitIn{}))
@@ -753,7 +758,8 @@ type InitOut struct {
 	TimeGran            uint32
 	MaxPages            uint16
 	MapAlignment        uint16
-	Unused              [8]uint32
+	Flags2              uint32
+	Unused              [7]uint32
 }
 
 type InterruptIn struct {
diff --git a/mount_config.go b/mount_config.go
index f95895ad..8f629430 100644
--- a/mount_config.go
+++ b/mount_config.go
@@ -221,6 +221,9 @@ type MountConfig struct {
 	// use ReaddirPlus for directory listing.
 	EnableAutoReaddirplus bool
 
+	// Flag to allow mmap() with MAP_SHARED for files opened with OpenDirectIO
+	AllowDirectIOMmap bool
+
 	// UseVectoredRead is a legacy flag kept for backward compatibility. It is now a no-op.
 	//
 	// The term vectored read was a misnomer for this flag. Its actual meaning was that
diff --git a/ops.go b/ops.go
index fe21a64f..725cd87b 100644
--- a/ops.go
+++ b/ops.go
@@ -35,12 +35,13 @@ type interruptOp struct {
 type initOp struct {
 	// In
 	Kernel fusekernel.Protocol
-
-	// In/out
-	Flags fusekernel.InitFlags
+	Flags  fusekernel.InitFlags
+	Flags2 fusekernel.InitFlags2
 
 	// Out
 	Library       fusekernel.Protocol
+	OutFlags      fusekernel.InitFlags
+	OutFlags2     fusekernel.InitFlags2
 	MaxReadahead  uint32
 	MaxBackground uint16
 	MaxWrite      uint32