Sure it could definitely have multiple meanings. The poem, written by Pat Mora, explores some of her own experiences as an American born to Mexican parents. In it, Mora describes how she feels that she is a part of both Mexican and American cultures, while at the same time feeling like she is distanced from both cultures.
A reader could take the poem to be the single, isolated lament of a particular person. The poem talks about a person who has a job in an office where he/she speaks English, but is capable of ordering food in Spanish. That person is a part of 2 cultures but feels separated from both. The reader could assume that the poem is the author venting about his/her individual frustrations. The reader could feel badly about it, but conclude it's not a big picture issue that affects multiple people.
On the other hand, a reader could interpret the poem as a representation of how an entire emerging culture is feeling. By being a second generation Mexican American, the speaker is quite comfortable speaking in both languages, and operating comfortably within both cultural norms. Despite the poet's adaptability though, he/she feels segregated from both cultures. An outsider. The reader could interpret the poem as an illustration of what an entire culture may be experiencing as well as other cultures that have come to America.
Personally, I think it is the latter. I think Mora is attempting to speak out on behalf of others like her. I think she is giving voice to the feelings that many current Mexican American people are feeling. They have their feet in both worlds and therefore struggle to be a 100% part of both.