Target (NYSE:TGT) (otherwise known as Tar-Zsay) really has a lot going for it. Clever ad campaigns. A clean and recognizable logo. World-renowned designers such as Jason Wu clamoring for partnerships. And plenty of fans, anecdotally speaking. Via its network of 1,763 stores, TGT has attracted 10.6 million fans on Facebook. Wal-Mart Stores (NYSE:WMT) has 14.4 million Facebook fans, but with quintuple the number of store locations.

Earning have been on the rise at TGT but appear to be leveling off. After an average year-over-year earnings gain of 13% from 2006 through 2012 (excluding an annual sales drop in 2009 after the 2008 bear market), annual earnings are projected to be unchanged in 2013 at $4.27 per share.

The same stagnancy is true with store expansion. After growing by leaps and bounds for decades — roughly 500 stores in 1995, 800 in 2000, 1,000 in 2003 — the chain seems to have hit a size that’s just right. In 2008, it had 1,682 stores. Today, there are 1,763, for a growth rate of 4.8% in the last five years.

In short, it’s beginning to look like Target could be reaching a critical point in its history. The chain is 50 years old this year, and it may be getting too big to grow further. It does, however, need to do something to keep earnings momentum moving in the right direction. Last week, TGT said same-store sales for March rose 7.3%, topping expectations. The company also upped its first-quarter earnings outlook.

So how can Target keep this trend alive, continuing to attract new customers without taking hammer to nail? And without drastically lowering prices? After all, a retailer can cut prices only so deep before cutting into the bottom line. Here are a few experiments the retailer is already implementing:

Partnering with the Almighty Apple

Apple (NASDAQ:AAPL) is planning a slow roll out of stores-within-a-store at Target locations, similar to what is currently in place at Best Buy (NYSE:BBY). The expansion would reportedly allow TGT to sell Mac computers in addition to the iPhones, iPods and iPads it currently stocks.

This could be a win-win, as it exposes Apple to a broader audience in markets where there may not be an Apple store. It also brings Applephiles into Target, where they might pick up some toiletries or groceries along with their newest Apple device. 

Expanding Its Edible Offerings

Speaking of groceries, Target is expanding its food selections, bringing more fresh produce, meats and baked goods onto its shelves. The retailer’s senior VP for the grocery division says this enhancement allows customers to “experience the added convenience of one-stop shopping” as they “stock up on all of their essentials.” 

Compartmentalization

Along with the Apple announcement, Target said it was planning a new layout called The Shops at Target that would offer boutique-style shopping experiences within its existing stores. For example, a customer could stop by one area featuring designer-label clothing and then hit a pet-centric boutique. This plan is for a limited-time basis but would likely continue if popular among Target shoppers.   

Tapping Into an Urban Customer Base

OK, so this requires some hammer and nails, but it’s a way Target can go head-to-head with Wal-Mart in pursuit of the city-dwelling consumer. The CityTarget concept will be introduced this year, with locations cropping up in L.A., Chicago, San Francisco and Seattle.

The idea is similar to the Wal-Mart Express model, which features small stores jam-packed with essentials for the home — groceries, housewares and some clothing. A CityTarget’s sales floor will be approximately 55,000 square feet compared to the average store, which is 95,000 to 135,000 square feet.

TGT shares are up roughly 10% so far this year, narrowly outperforming the broader market. Over the past five years, however, TGT shares are down almost 8%. The stock has been unable to muster a convincing move above the $60 level since late 2007.

As of this writing, Beth Gaston Moon owns share of Apple (AAPL).