This may not be built-in, but we can achieve this by setting the row to not require a response and giving the grid question this custom verification:
// Parameters
var otherSpecifyRow = 4;
var errorMessage = 'Error...';
// Run
if (SSI_GetValue('[% QuestionName() %]_r' + otherSpecifyRow + '_other')) {
$('input[name="hid_col_list_[% QuestionName() %]"]').val().split(',').forEach(function(column){
if (!SSI_GetValue('[% QuestionName() %]_r' + otherSpecifyRow + '_c' + column)) {
strErrorMessage = errorMessage;
}
});
}
Lines 2 and 3 should be updated to fit your needs.