Yes. My father was adopted and I'm also searching for his birth family.
However, the more testing services you use, the greater the pool of prospects. Since you've started with 23& Me, the next step is to go to FTDNA and order both the Family Finder and (at least 67-marker) yDNA tests.
If you get lucky and find a yDNA match, you can reach out to the match(es) for information on their direct paternal ancestor if it is not already in their profile, or you can join a yDNA surname project. Even if there isn't a project established with your surname, there are many location and ethnicity projects as well, so join as many as you can. Even if you don't find a surname match (many times due to non-paternal events and adoptions), a lot of yDNA projects publish lineages that your kit may fall under and the lineages will point you in the direction of further research. Keep in mind that it could take years before you find a match - my brother's yDNA match was a member of FTDNA for 4 years before he had a hit with my brother.
The Family Finder test is the same test as Ancestry and 23&Me and is available in Canada. These tests will compare the DNA of males and females, so you'll end up with thousands of new cousins and it's much, much more easier and efficient to find and compare specific surnames. Some folks attach gedcoms to their kits. FTDNA's gedcoms are very basic and not pretty, but they are still useful. For easier use, an FTDNA gedcom can be snagged using this website:
http://kelleyllc.com/ftdna-gedcom/ and then it can be imported into Ancestry or a genealogy software.
Family Finder also provides a chromosome browser so you can identify the chromosome and segment of DNA you share with your matches. With a little research, you may be able to find a couple matches that share the same common ancestor and DNA segment, which will give you further evidence of your descendancy. My 23&Me kit is currently being processed, so I can't yet comment on the 23&Me experience, but it is my understanding that since it is more of scientific site (having been established to identify medical propensities), that many users are not necessarily interested in genealogy and the community is not as open to collaboration as FTDNA or Ancestry. Also, messaging and emails addresses are not provided, so requests have to be made in order to establish contact.
Both 23 and Me and FTDNA will let you download your raw data, which is highly recommended. Once you get your raw data, you can upload it to GEDMatch - a free site run by volunteers. There are several tools available there to further your DNA research, but one of the greatest benefits is that it accepts data from all services: FTDNA, 23 and Me and Ancestry - so while you may not be able to purchase an Ancestry test, you can still at least collaborate with US Ancestry members who have uploaded their kits to GEDMatch.
If you find yourself buying up all the different kits and services, I recommend downloading Genome Mate to manage all your matches into one database. It is free and the angel who built and maintains it is dedicated and responsive.
Finally, there are some great forums here that you should browse and set as favorites: Autosomal DNA, General Research and GedMatch. There are angels that post on these boards frequently that are much more experienced and eloquent than I and can give you excellent direction, tips, tools and guidance for further research. Look for threads with technical guidance and lots of responses - particularly from late 2012 and on (when Ancestry finally allowed us to download our raw data) - you're guaranteed to find very useful information.
Good luck!