Source: Papa Murphy's.

Investors looking to grab a slice of the pizza market seemingly have no shortage of possibilities, as the rush to make every corner pizza joint the next "Chipotle of Pizza" gains momentum.

The latest pizza joint looking to cash in on the pizzeria-as-fast-casual restaurant fad is Papa Murphy's, which is set to go public this Friday with initial pricing for its shares in the range of $11 to $13 a slice -- er, stub. It comes amid a crush of restaurants looking to feed off investor appetite for restaurant stocks. A few weeks ago, Mediterranean-inspired shop Zoe's Kitchen went public, raising almost $88 million, and soon we're likely to see regional Mexican restaurant chains Cafe Rio and El Pollo Loco, a grilled chicken joint, both ride the coattails of fast-casual cuisine.

But pizza has gained particular cachet as the next big boom in quick-serve dining. An explosion of high-minded-concept pizza shops are trying to recreate the Chipotle Mexican Grill (CMG -1.34%) experience in a pizza joint, with places like Blaze Pizza, Pie Five, and PizzaRev trying to expand their brands

Papa Murphy's looks to differentiate itself from the pack by also offering fresh ingredients and a make-your-own-pie experience by only preparing the pie -- customers then take it home and bake it themselves afterward. It's kind of like a frozen pie without the freezer. That freshness is evident with its anticipated ticker symbol on the Nasdaq exchange: FRSH.

Yet I'm not certain the fast-casual pizza fad has legs to grow much further. Pizza caters primarily to young males between ages 6 and 19, not exactly the nouveau pizza demographic, and the market researchers at NPD Group say that while the pizza business was expected to grow 2.3% in 2013, that's down from the 3.7% growth it achieved the year before -- but won't be as low as this year, when sales are expected to widen less than 2%.

While the fast-casual niche has proven to be the only restaurant segment recording any growth at all, the inundation of concepts, from new entrants to established players trying to make up for falling sales elsewhere in their operations, means the market will be flooded with choices for consumers, giving few chains a chance to stand out. 

Papa Murphy's was founded in 1981 and has grown to over 1,400 stores in 38 states, Canada, and the United Arab Emirates, some 95% of which are franchised. Revenues hit $785.6 million last year, representing a better than 8% compounded annual growth rate over the last decade. Even so, much of that growth is fueled by its adding more stores to the chain. Comparables, or sales at restaurants opened at least a year, were up 5.7% back in 2011, but they fell to less than half of that last year.

In contrast Chipotle Mexican Grill has enjoyed compounded growth of over 26% annually for the past 10 years, sales were up another 24% this past quarter, and comparables were up more than 13%, better than the 9% increase seen in the fourth quarter and the 5.6% rise seen across 2013. And it's getting into the business too, with a partnership with Pizzeria Locale.

Like Papa Murphy's, Zoe's Kitchen initially priced its offering at $11 to $13, but raised it by $2 a share at the end -- yet still managed to close its first day of trading 73% higher, suggesting it may have left some money on the table. Papa Murphy's may be a bit conservative, and I wouldn't be surprised if it had a similarly successful IPO, but I'm still wary that all these restaurants going public in the same niche is simply too much of a good thing.

Pizza may be hot, and there's something to the notion it can do fast-casual too -- I'd put my money on Chipotle getting it right -- but I'll continue avoiding the stocks of these new pizza parlors and pick up a slice as well at my corner pizza joint instead.