Hey In my knowledge we can do it not same as you mentioned in your question but yes likely we can do it as:
$collection->addAttributeToFilter(
array(
array('attribute'=> 'someattribute','like' => 'value'),
array('attribute'=> 'otherattribute','like' => 'value'),
array('attribute'=> 'anotherattribute','like' => 'value'),
)
);
here in array we need to specify the attribute and value and it will give you output as in where clause like:
WHERE ((someattribute LIKE 'value') OR (otherattribute LIKE 'value') OR (anotherattribute LIKE 'value'))
For more information you can look into this answer too.Hope this help.