MySQL where clause with conditions based on other columns

I apologise for the vagueness of the title, but I couldn't find a better way. There's this MySQL table which consists of entity config mapping in a flattened structure.

CREATE TABLE entity_config (
  id int unsigned NOT NULL AUTO_INCREMENT,
  entity_id bigint NOT NULL,
  config_id bigint NOT NULL,
  config_value bigint NOT NULL,
  PRIMARY KEY (id),
  KEY entityconfig_entity_id_config_id_config_value (entity_id,config_id,config_value),
  KEY idx_config_id_config_value (config_id,config_value),
) ENGINE=InnoDB AUTO_INCREMENT=17382 DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_0900_ai_ci

Apart from the id, there are 2 composite indexes on (entity_id, config_id, config_value) and (config_id, config_value). We have to support filter/search queries based on both config_id and config_value in the following way - Find all entity_ids that have config_id=10 and config_value=1000 and also config_id=20 and config_value=5000 The simplest way to do this is via joins

select ec1.entity_id 
from entity_config ec1 
inner join entity_config ec2 on ec1.entity_id = entity_id 
where ec1.config_id=10 
and ec1.config_value=1000 
and ec2.config_id=20 
and ec2.config_value=5000

1 join is fine but the more configs the customer wants to search, we'll have to keep adding joins and it can come to a point where we're joining the table with itself 10 times just because of 10 filters by the customer. I tried to use case when then inside the where clause like so

select entity_id from entity_config
where (
   case when config_id=10 then config_value = 1000 when config_id=20 then config_value=5000 end
)

But this is just an OR condition which gives entity_ids that have EITHER the 1st config combo or the 2nd one. Does anyone know any better or more efficient way of solving this? Thank you!