Should company A have different social network identities for each service/website?

I agree with Jarie. If possible, you should stick with one FB page, Twitter account, etc. Work on branding your company first, then the particular services you offer. In today's noisy landscape, it's tough to get awareness for one thing, let alone three or four. I would figure out what your 'one thing' is - e.g. what makes you different and unique - and integrate messaging points from across your service lines.

That said, Avelle has done a nice job of offering several different accounts for various offerings. They are quite different though as they deal in rentals of luxury handbags and accessories.

I think it all depends on the theme of the services. If they generally have the same theme, then I would build one brand around the company and have the services as sub-brands. Some examples of this are The Omni Group who have a suite of tools that center around productivity and creative pursuits. It's kind of a loose theme but it works for them.

Another example would be 37 Signals. There theme is simple small business software but they only have a single Facebook fan page and their services are sub-brands.

One thing to keep in mind is that if you have fans of your products, they could build their own sites as an offshoot and refer to your main companies site for inspiration.

If you have multiple products and they have a similar theme, then having one company site makes sense. If they are so different that it would confuse people, then having separate ones is the way to go. Remember that you want to build your companies brand as well and the best way to do that is to have a consistent message and then sub-brand your services.

The question is one of scale. If your company has just a few hundred fans then you might be as well to keep them all in one place so that you have a sense of community and build social proof into you many brands.

I always advise companies to use the home and hub approach. First you build your home- the place where all the brands live. As they grow up they branch out, maybe they get their own blog category and (semi automated from that category) twitter account. As they continue to grow they gain their own domain name or sub domain onto which goes the blog that has grown from the category on the home domain. This new blog should be quickly populated with content and must be maintained so it is best to launch only if there is enough to say.

Once the brand has a fully content powered hub then there is something to say for starting a new point of contact. Each point of contact points to the hub and each hub points to the home. The home starts to be more and more the gist and summary place where the detailed stuff happens on the hubs.

Hubs are, then, dictated by how much time you can dedicate the to the brand.

So lets say you are ready for the new brand Facebook page. Each new item for the brand needs to be pushed from home and from the other points of contact and the Facebook page is no different. You want a short time from launch to sense of community. I find that automating some posting from blog headlines to social media helps keep the content flowing.

But ever new Point of Contact means people that someone has to interact with, supply content for and invest time and effort into. Only do this for brands for which there is a ROI for this investment.

That said there is sometimes no harm in creating passive brand grabs - twitter, facebook, domain registrations meant only to stop someone one else getting there first and allowing the crowd to react to this passive entity if they want. However the ROI is worse and the launch to active harder.

On the whole I would say anything you can create a buzz around might give you good ROI on starting a hub and giving it multiple points of contact.