How to configure the intermediate output directory in C#

You could try to do this (don’t forget that there are Debug and Release sections which will be used depending on what type of build you are targeting):

<PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">
    ...
    <BaseIntermediateOutputPath>..\build\obj</BaseIntermediateOutputPath>
    <IntermediateOutputPath>$(BaseIntermediateOutputPath)$(Configuration)\</IntermediateOutputPath>
</PropertyGroup>
<PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|AnyCPU' ">
    ...
    <BaseIntermediateOutputPath>..\build\obj</BaseIntermediateOutputPath>
    <IntermediateOutputPath>$(BaseIntermediateOutputPath)$(Configuration)\</IntermediateOutputPath>
</PropertyGroup>