How do we implement not only interface inheritance but also multiple implementation inheritance in objective-c?

Question

This is my strategy so far:

I declared this protocol:

@protocol BGSuperSingletonProtocol <NSObject>
+(id) singleton1;
+(instancetype)singleton;
@end

Then I created a category where all NSObject support that protocol. However, I do not want all NSObject to support that protocol. I just want some NSObject to do. So I will insert this header in .m files rather than .h files

#import "BGSuperSingletonProtocol.h"

@interface NSObject (singleton) <BGSuperSingletonProtocol>

@end

Then I write the implementation of that category

#import "NSObject+singleton.h"

@implementation NSObject (singleton)

static NSMutableDictionary * allTheSingletons;

+(instancetype)singleton
{
    return [self singleton1];
}
+(id) singleton1
{
    NSString* className = NSStringFromClass([self class]);

    if (!allTheSingletons)
    {
        allTheSingletons = NSMutableDictionary.dictionary;
    }

    id result = allTheSingletons[className];

    //PO1(result);
    if (result==nil)
    {
        result = [[[self class] alloc]init];
        allTheSingletons[className]=result;
        [result additionalInitialization];
    }
    return result;
}

-(void) additionalInitialization
{

}