Magento2: How to add multiple AND and OR conditions to filter/filterGroups?

Yes it is possible

You can create an

\Magento\Framework\Api\SearchCriteriaBuilder $searchCriteriaBuilder
\Magento\Framework\Api\FilterBuilder $filterBuilder
\Magento\Framework\Api\Search\FilterGroupBuilder $filterGroupBuilder

After that define your filters

// AND
$this->searchCriteriaBuilder->addFilter('attribute1','value2');
$this->searchCriteriaBuilder->addFilter('attribute2','value2');

// OR
$attr3 = $this->filterBuilder->setField('attribute3')
            ->setValue('value3')
            ->setConditionType('eq')
            ->create();
$attr4 = $this->filterBuilder->setField('attribute4')
            ->setValue('value4')
            ->setConditionType('eq')
            ->create();

 $filterOr = $this->filterGroupBuilder
            ->addFilter($attr3)
            ->addFilter($attr4)
            ->create();
 $this->searchCriteriaBuilder->setFilterGroups([$filterOr]);

 $searchCriteria = $this->searchCriteriaBuilder->create();

 $this->productRepository->getList($searchCriteria);

GET ==>

attribute1 = 'value1' AND attribute2 = 'value2' AND (attribute3='value3' OR attribute4 = 'value4')

Tell me if you have any other questions

    $attr1 = $this->filterBuilder->setField('attribute1')
        ->setValue('value1')
        ->setConditionType('eq')
        ->create();
    $attr2 = $this->filterBuilder->setField('attribute2')
        ->setValue('value2')
        ->setConditionType('eq')
        ->create();

    $filterOr1 = $this->filterGroupBuilder
        ->addFilter($attr1)
        ->addFilter($attr2)
        ->create();


    $attr3 = $this->filterBuilder->setField('attribute3')
        ->setValue('value3')
        ->setConditionType('eq')
        ->create();
    $attr4 = $this->filterBuilder->setField('attribute4')
        ->setValue('value4')
        ->setConditionType('eq')
        ->create();

    $filterOr2 = $this->filterGroupBuilder
        ->addFilter($attr3)
        ->addFilter($attr4)
        ->create();

    $this->searchCriteriaBuilder->setFilterGroups([$filterOr, $filterOr2]);

    $searchCriteria = $this->searchCriteriaBuilder->create();

    $this->productRepository->getList($searchCriteria);

GET ==>

(attribute1 = 'value1' OR attribute2 = 'value2') AND (attribute3='value3' OR attribute4 = 'value4')