How to do it right in terms of BEM?

Question

css

Good evening.
There is a large block (slider) that has several types and layouts. Each type has unique elements, and each type has common elements. I solved the problem by creating one common block, and two specific blocks, which I then mixed.

The code for this whole thing

<!-- Первый слайдер -->
<div class="slider slider-promo">
    <div class="slider__track slider-promo__track">
        <div class="slider__slide slider-promo__slide"></div>
        <div class="slider__slide slider-promo__slide"></div>
        <div class="slider__slide slider-promo__slide"></div>
    </div>

    <div class="slider__arrows slider-promo__arrows"></div>
</div>

<!-- Второй слайдер -->
<div class="slider slider-grid">

    <!-- Набор уникальных для второго слайдера элементов -->
    <div class="slider-grid__meta">
        <div class="slider-grid__description"></div>
    </div> 

    <div class="slider__track slider-grid__track">
        <div class="slider__slide slider-grid__slide"></div>
        <div class="slider__slide slider-grid__slide"></div>
        <div class="slider__slide slider-grid__slide"></div>
    </div>

    <div class="slider__arrows slider-grid__arrows"></div>
</div>

Questions:
- Is it possible to assign only the class of this very specific block to elements unique for each specific block? As in the code above, I didn't give the .slider-grid__meta element the .slider__meta class.
- Can it be prettier? There is such a feeling as if he had put on crutches. How would you accomplish a similar task?
Thanks in advance.