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I reread the thread and noticed that you are using product variant customfields. There are a few more steps but the concept is the same.

This code would live in your Basket / TOE_Basket template. You will have to modify the code to use your customfield code and value.

You'll also have to test the code because each store's variants can be built differently.

<mvt:foreach iterator="item" array="basket:groups">

//

<mvt:do name="l.return" file="g.Module_Library_DB" value="Runtime_Product_Load_Code( l.settings:item:code, l.settings:product )" />
<mvt:do file="g.Module_Library_Utilities" name="g.has_variant_with_options" value="OrderItem_DetermineVariant_WithOptions(l.settings:item, l.settings:item:options, l.settings:item:option_count, l.settings:product, g.variant_id)" />
<mvt:do file="g.Module_Library_DB" name="l.success" value="ProductList_Load_Variant(l.settings:product:id, g.variant_id, l.settings:productvariants)" />
<mvt:foreach iterator="part" array="productvariants">
<mvt:assign name="g.product_part_id" value="l.settings:part:id" />
</mvt:foreach>
<mvt:do name="l.return" file="g.Module_Library_DB" value="Product_Load_ID( g.product_part_id, l.settings:variant_product )" />
<mvt:if expr="NOT ISNULL l.settings:variant_product:id">
<mvt:do file="g.Module_Root $ '/modules/util/customfld.mvc'" name="g.has_variant_custom_field" value="ProductFieldValue_Load_CodeAndProduct( 'availability', l.settings:variant_product:id, l.field, l.settings:availability)" />
<mvt:assign name="g.has_availabilty" value="l.settings:availability" />
</mvt:if>

<mvt:if expr="g.has_availabilty EQ 'In Stock'" />

// Do In stock Stuff Here

<mvt:else>

// Do Out Of Stock Stuff Here

</mvt:if>

//

</mvt:foreach>