Yes that can happen, but you have to structure it properly. There's two simple ways to do it:

1-VARYING BUSINESS TYPES: instead of only going after the fine dining, or the same niche of Italian restaurants as a client, get different types of businesses. Mexican place, Italian place, maybe the fast food spot.. But don't do 2 of the same type restaurants IF it's within close proximity .

Q: WHAT IF YOU ARE MARKETING IN A BIG AREA, IS IT THEN OK TO DO MULTIPLE BUSINESSES OF SAME TYPE?

Q: Yes. Larger cities where it takes 30 min or more to go just 10 miles, it's acceptable. The two same places won't cross paths. You can even take the same concept of varying businesses within a niche and do the method for other niches: ex- the restaurant, the driving range, the car wash.

When you think about it from this perspective, it only adds MORE value to the potential customers you're marketing to- more gifts for them during their birthday week :)

2-THE DIRECTORY: We built this if you ever encounter that issue of close proximity, and multiple business types. The way you structure it if leading with a birthday ad is as follows:

-ANCHOR AD: This is your main restaurant

-Directory Ads: These are the businesses in the directory. You'd charge less as their would be more options for consumer ot choose from.. You make up for lesser price with volume of offers. good range $77-$97/m per directory listing. 

MAIN AD: $500/M
DIRECTORY ADS: $$77-$97/M

Hope that helps. 

I recommend just GET STARTED, and address that good problem when it happens. Once it does, just know there's a solution for it :)