Inner Wrapper for a block

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I would like to create an Inner wrapper for any block, so that when a style is set to a block the wrapper is on the inside, something like this:

<div id="id_set_in_block_design" style="style_set_in_design">
<div class="my_inner_wrapper">
block content
</div>
<div>

blockWrapperStart does that but on the out side, and same for Jordan Lev's Block Wrapper Templates

 
ScottSandbakken replied on at Permalink Reply
ScottSandbakken
This would be done in the block template.
guyDesign replied on at Permalink Reply
I would like to apply it globally to any block.