Могу ли я использовать один BehaviorSubject для нескольких событий?

Самый простой способ — создать тип CustomEvent (не буду называть его Event, так как этот тип уже используется). Вы можете либо дать ему поле eventType, либо использовать классы, которые расширяются от этого CustomEvent, чтобы различать, какой тип события используется.

1. eventType поле

events.ts

export interface CustomEvent{
   eventType: 'Update' | 'OtherEvent';
   data: any; // Type unsafe, maybe narrow it down
}

Прокси события

export class EventProxyService {
    private eventTracker = new BehaviorSubject<CustomEvent>(undefined);
    getEvent(): BehaviorSubject<CustomEvent> { return this.eventTracker; }
    setEvent(param: CustomEvent): void { this.eventTracker.next(param); }
}

добавлять/получать события

// Services omitted, too long
// add new event
this.eventProxyService.setEvent({
    eventType: 'Update',
    data: {/* Your data here */}
});

// listen to events
this.subscription = this.eventProxyService.getEvent()
    // .filter(param => param.evenType === 'Update') // if you want only specific events
    .subscribe((param: CustomEvent) => {
        if (param.eventType === 'Update') {
            this.theTargetMethod(param);
        } else if (param.eventType === 'OtherEvent') {
            // do something else
        }
    );

2. Классы событий

events.ts

export class CustomEvent {}
export class UpdateEvent extends CustomEvent {
   constructor(
      public newData: Data // Use a specific type and as many fields as you need
   ) {}

}
export class OtherEvent extends CustomEvent {
   constructor(
      public otherData: OtherData// Use a specific type and as many fields as you need
   ) {}
}

Прокси события

export class EventProxyService {
    private eventTracker = new BehaviorSubject<CustomEvent>(undefined);
    getEvent(): BehaviorSubject<CustomEvent> { return this.eventTracker; }
    setEvent(param: CustomEvent): void { this.eventTracker.next(param); }
}

добавлять/получать события

// Services omitted, too long
// add new event
this.eventProxyService.setEvent(new UpdateEvent({
   /* Your data here */
}));

// listen to events
this.subscription = this.eventProxyService.getEvent()
    // .filter(param => param instanceof UpdateEvent) // if you want only specific events
    .subscribe((param: CustomEvent) => {
        if (param instanceof UpdateEvent) {
            this.theTargetMethod(param);
        } else if (param instanceof OtherEvent) {
            // do something else
        }
    );

3. Несколько предметов

Прокси события

export type EventType: 'update' | 'other';

export class EventProxyService {
    // Use BehaviourSubject<SPECIFIC_TYPE> if possible
    private updateEventTracker = new BehaviorSubject<any>(undefined);
    private otherEventTracker = new BehaviorSubject<any>(undefined);

    setEvent(type: EventType, param: any): void { 
        this.getEventTrackerForType(type).next(param);
    }
    getEvent(type?: EventType): BehaviorSubject<any> { 
        return this.getEventTrackerForType(type);
    }

    private getEventTrackerForType(type?:EventType): BehaviorSubject<any> {
        switch(type) {
            case 'update': return this.updateEventTracker;
            case 'other': return this.otherEventTracker;
            // if no type specified, return ALL events as one Observable (bonus)
            default: return merge(
                this.updateEventTracker, 
                this.otherEventTracker
            )
        }
    }

    // alternatively, create setEvent/getEvent methods for each subject specifically (setUpdateEvent/getUpdateEvent/...)
}