actionRelationships - requires https://github.com/yii2tech/ar-linkmany - works almost as described in http://stackoverflow.com/questions/6324547/how-to-handle-many-to-many-relationships-in-a-restful-api#answer-6328012

ImageController.php

<?php
class ImageController extends \yii\rest\ActiveController
{
    public $modelClass = 'app\models\Image';
    public $relationAttribute = 'imageIds';
    public $relations  = [
        'tags' => 'tag_id',
        'owner'  => 'owner_id'
    ];
    public function actionRelationships($id = '')
    {
        $ids = preg_split('/\s*,\s*/', $id, -1, PREG_SPLIT_NO_EMPTY);
        $verb = Yii::$app->request->method;
        $queryParams = Yii::$app->request->queryParams;
        $modelClass = new $this->modelClass;
        $linked = false;
        foreach ($queryParams as $key => $value) 
        {
            if(!is_scalar($key) or !is_scalar($value))
                throw new BadRequestHttpException('Bad Request');
            else if (in_array(strtolower($key), $this->relations)) 
            {
                $name = array_search($key, $this->relations);
                $relation = $modelClass->getRelation($name);
                if ($relation !== null) 
                {
                    $relatedModelClass = new $relation->modelClass;
                    $relatedModel = $relatedModelClass::findOne($value);
                    if (is_null($relatedModel)) throw new NotFoundHttpException("Object not found: $value");
                    if ($relation->multiple === false)
                    {
                        if (isset($relatedModel->{$this->relationAttribute}) && is_array($relatedModel->{$this->relationAttribute}))
                        {
                            // one_to_many relation
                            if ($verb === 'PATCH') {
                                $relatedModel->{$this->relationAttribute} = array_merge($relatedModel->{$this->relationAttribute}, $ids);
                                if ($relatedModel->save() === false && !$model->hasErrors())
                                    throw new \yii\web\ServerErrorHttpException('Failed to link objects for unknown reason.');
                                $linked = true;
                            }
                            else throw new \yii\web\ForbiddenHttpException('Not allowed due to objects relation nature');
                        }
                    }
                    else if ($relation->multiple === true && $relation->via !== null)
                    {
                        // many_to_many relation
                        if ($verb === 'PUT') $relatedModel->{$this->relationAttribute} = $ids;
                        else if ($verb === 'PATCH') $relatedModel->{$this->relationAttribute} = array_merge($relatedModel->{$this->relationAttribute}, $ids);
                        else if ($verb === 'DELETE') {
                            if (empty($ids)) $relatedModel->{$this->relationAttribute} = $ids;
                            else {
                                $newIds = array_values(array_diff($relatedModel->{$this->relationAttribute}, $ids));
                                $relatedModel->{$this->relationAttribute} = $newIds;
                            }
                        }
                        if ($relatedModel->save() === false && !$model->hasErrors())
                            throw new \yii\web\ServerErrorHttpException('Failed to link objects for unknown reason.');
                        $linked = true;
                    }
                }
            }
        }
        $linked === true ? Yii::$app->Response->setStatusCode(204) : Yii::$app->Response->setStatusCode(304);
    }