One of yesterday's market winners was Applebee's (NASDAQ:APPB), jumping 4% higher after Bloomberg reported that IHOP (NYSE:IHP) may be a participant in the second round of bidding for the languishing casual dining operator.

Citing "people familiar with the matter," the story claimed that IHOP was offering more than $2 billion for the chain that put itself on the block earlier this year.

This smells as fruity as a Rooty Tooty Fresh 'N Fruity, the more I think about it. Sure, IHOP CEO Julia Stewart worked at Applebee's several years ago. That seems to be about the only thing that makes sense in this potential pairing.

I have no doubt that Applebee's will find a suitor, though my gut tells me that it will come from private equity circles. The combination of IHOP, a breakfast specialist, and a lunch and dinner heavyweight like Applebee's would accomplish what, exactly? Can anyone picture an IHOP/Applebee's multi-concept unit under the same roof to make the most of all three dayparts? Fast-food chains like Yum! Brands (NYSE:YUM) can pull this off, but it's just not feasible on the casual dining side. You can't risk the brand dilution at the table service level.

Naturally, the allure here is that a pair of franchise-driven companies can work through economies of scale, with each brand catering to its specific audience. We'd be talking about an empire of more than 3,000 restaurants. That's a lot of butter pecan syrup and fiesta lime chicken! But how can a company like IHOP afford to even lift up a bidding card at this particular auction? The already-leveraged IHOP commands half the market cap of Applebee's, and two-thirds of its enterprise value.

Oh, and these two aren't exactly cut from the same franchise show cloth. More than 99% of the IHOP restaurants -- all but 13 -- are franchised or licensed locations, whereas Applebee's owns 27% of its eateries.

Does IHOP envision itself as a casual dining operator, or is the plan here to sell off the company-owned Applebee's units as a way to partly finance the sale? If it's the latter, the timing couldn't be any worse. Nervous existing or potential franchisees would demand fire sale prices ... and they'd probably get them.

The seed of IHOP's discontent
One could argue that IHOP doesn't need another concept. Despite spotty earnings growth lately, the pancake-powered namesake chain has delivered 17 consecutive quarters of positive comps.

That's a pretty impressive streak, especially when so many of the conventional casual dining eateries have stumbled in recent quarters. Applebee's had a jaw-dropping streak of 31 consecutive quarters with positive unit-level gains end last year. It has gone on to post negative comps in each of the past four quarters.

IHOP's store-level popularity is making it an easy sell to franchisees. While some of the leading fast-food burger chains and casual-dining blue chips have fewer locations open today than they did a year ago, IHOP has grown its reach by 54 units over the past year.

So why did IHOP announce that it was on the prowl for an acquisition earlier this year? My guess is that the company wants to kick up its growth rate, but acquiring a smaller franchise-fueled concept like Jamba Juice (NASDAQ:JMBA), Cinnabon, or Caribou Coffee (NASDAQ:CBOU) would be a more economical fit, that would just happen to create synergistic opportunities under the same roof for more adventurous franchisees.

So take down that bidding card, IHOP. You don't need Applebee's. You know you don't.

Other quick bites off the Foolish menu:

Longtime Fool contributor Rick Munarriz is a casual diner at both IHOP and Applebee's. He does own shares in Jamba Juice. He is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early. The Fool has a disclosure policy.