Most Novus Ordo parishes combines all the different stipends into a single mass (you can see the long list of intentions in their bulletins). This itself is a scandal because a priest can only take 1 stipend per Mass.
I routinely go to Sunday Mass at three different parishes (due to work schedule / Mass schedule / travel / TLM being offered) and Confession in four different parishes (due to schedule, especially as a couple offer weekday evening Confessions and one on Saturday mornings, which is convenient). These parishes are in three different dioceses (Spokane and Yakima (WA), Boise (ID). I always pick up a bulletin (many will have a rack with the current and past week's bulletins). I have NEVER, EVER seen multiple intentions for a single Mass, EVER.
What might be the situation, maybe, is that most parishes have multiple Masses on Sunday. My parish has eight Masses every weekend, in English and Spanish. Most (unless it has a single priest covering another parish or mission) will have a daily Mass Monday through Saturday. If there is more than one priest they may have additional daily Masses (i.e. 5:30 or 6 AM for the before work crowd, 5:30 PM for the after-work crowd, a mid-morning school Mass, a mid-day senior citizen Mass with lunch and a program, etc.). If one were to actually read the bulletin they probably may notice that the each from the "long list of intentions" was assigned to a particular Mass. One Mass each Sunday is "Pro Populo", offered for the entire parish community, which is required by the Church. It is usually the principal Sunday morning Mass.
One thing that recently changed in my parish could be confusing, if one hadn't seen the pastor's article in the bulletin about it. In some cultures there is a misguided view that the one who pays the Mass stipend somehow "owns" the Mass (and they may like to have it announced at the Mass that they are "sponsoring" it). Besides the appearance of simony, it is the priest who is offering his intention for the family, it's not the family's Mass. So now, each daily Mass has its (the offering priest's) intention listed in the bulletin but for Sunday the entire intention list is shown without a designation of which Mass they are individually being offered at. The pastor added that if a particular date had a special significance (i.e. the anniversary of a marriage or death) the office would tell them which Sunday Mass was being offered for that intention, so they could attend that Mass if they wished.