diff --git a/pcsx2/GS/Renderers/DX11/GSDevice11.cpp b/pcsx2/GS/Renderers/DX11/GSDevice11.cpp
index 8ec5acf8d3..80dcfd1df3 100644
--- a/pcsx2/GS/Renderers/DX11/GSDevice11.cpp
+++ b/pcsx2/GS/Renderers/DX11/GSDevice11.cpp
@@ -2635,6 +2635,8 @@ void GSDevice11::RenderHW(GSHWDrawConfig& config)
 		}
 	}
 
+	// Destination Alpha Setup
+	const bool multidraw_fb_copy = m_features.multidraw_fb_copy && (config.require_one_barrier || config.require_full_barrier);
 	GSTexture* primid_texture = nullptr;
 	if (config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::PrimIDTracking)
 	{
@@ -2649,7 +2651,7 @@ void GSDevice11::RenderHW(GSHWDrawConfig& config)
 			primid_texture, GSVector4(config.drawarea), m_date.primid_init_ps[static_cast<u8>(config.datm)].get(), nullptr, false);
 	}
 	else if (config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::Stencil ||
-			 config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::StencilOne)
+			 (config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::StencilOne && !multidraw_fb_copy))
 		SetupDATE(colclip_rt ? colclip_rt : config.rt, config.ds, config.datm, config.drawarea);
 
 	if (config.vs.expand != GSHWDrawConfig::VSExpand::None)
@@ -2764,6 +2766,11 @@ void GSDevice11::RenderHW(GSHWDrawConfig& config)
 
 	OMSetRenderTargets(draw_rt, draw_ds, &config.scissor, read_only_dsv);
 	SetupOM(config.depth, OMBlendSelector(config.colormask, config.blend), config.blend.constant);
+
+	// Clear stencil as close as possible to the RT bind, to avoid framebuffer swaps.
+	if (config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::StencilOne && multidraw_fb_copy)
+		m_ctx->ClearDepthStencilView(*static_cast<GSTexture11*>(draw_ds), D3D11_CLEAR_STENCIL, 0.0f, 1);
+
 	SendHWDraw(config, draw_rt_clone, draw_rt, config.require_one_barrier, config.require_full_barrier, false);
 
 	if (config.blend_multi_pass.enable)
diff --git a/pcsx2/GS/Renderers/DX12/GSDevice12.cpp b/pcsx2/GS/Renderers/DX12/GSDevice12.cpp
index 4e3584d84a..1c27ce0765 100644
--- a/pcsx2/GS/Renderers/DX12/GSDevice12.cpp
+++ b/pcsx2/GS/Renderers/DX12/GSDevice12.cpp
@@ -3831,8 +3831,12 @@ GSTexture12* GSDevice12::SetupPrimitiveTrackingDATE(GSHWDrawConfig& config, Pipe
 void GSDevice12::RenderHW(GSHWDrawConfig& config)
 {
 	// Destination Alpha Setup
-	const bool stencil_DATE = (config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::Stencil ||
-							   config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::StencilOne);
+	const bool stencil_DATE_One = config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::StencilOne;
+	const bool stencil_DATE = (config.destination_alpha == GSHWDrawConfig::DestinationAlphaMode::Stencil || stencil_DATE_One);
+
+	// TODO: Backport from vk.
+	if (stencil_DATE_One)
+		config.ps.date = 0;
 
 	GSTexture12* colclip_rt = static_cast<GSTexture12*>(g_gs_device->GetColorClipTexture());
 	GSTexture12* draw_rt = static_cast<GSTexture12*>(config.rt);
diff --git a/pcsx2/GS/Renderers/HW/GSRendererHW.cpp b/pcsx2/GS/Renderers/HW/GSRendererHW.cpp
index 4ba5641a47..17c846f71c 100644
--- a/pcsx2/GS/Renderers/HW/GSRendererHW.cpp
+++ b/pcsx2/GS/Renderers/HW/GSRendererHW.cpp
@@ -7939,7 +7939,8 @@ __ri void GSRendererHW::DrawPrims(GSTextureCache::Target* rt, GSTextureCache::Ta
 	}
 	else if (DATE_one)
 	{
-		if (features.texture_barrier)
+		const bool multidraw_fb_copy = features.multidraw_fb_copy && (m_conf.require_one_barrier || m_conf.require_full_barrier);
+		if (features.texture_barrier || multidraw_fb_copy)
 		{
 			m_conf.require_one_barrier = true;
 			m_conf.ps.date = 5 + m_cached_ctx.TEST.DATM;