The question of whether the United States should allow more undocumented (often referred to as "illegal") immigrants is deeply divisive and complex. Arguments in this debate span a range of considerations, including economic, humanitarian, security, and cultural concerns. Here's a balanced overview of the primary arguments on both sides:

Arguments in Favor of Allowing More Undocumented Immigrants: 

1. Humanitarian Reasons: Advocates argue that many undocumented immigrants are fleeing dire circumstances, such as violence, poverty, or political persecution. Allowing them into the U.S. provides them with a chance at a better life.

2. Economic Contributions: Undocumented workers play significant roles in various industries, especially agriculture, construction, and hospitality. They contribute to the economy through consumption and taxes.

3. Demographic Considerations: With an aging population, younger immigrants can help offset demographic shifts, contributing to the labor force and supporting social safety nets.

4. Integration of Existing Populations: Many undocumented immigrants have been in the U.S. for years, if not decades, with families, jobs, and community ties. Some argue it's more pragmatic to offer pathways to legalization than to attempt large-scale deportations.

5. Reduction in Exploitation: By legitimizing the status of undocumented immigrants, they might be less vulnerable to exploitation, as they'd be more likely to report crimes and unfair labor practices without fear of deportation.

Arguments Against Allowing More Undocumented Immigrants: 

1. Rule of Law: Critics argue that allowing more undocumented immigrants or providing amnesty undermines the rule of law and might incentivize future illegal immigration.

2. Economic Concerns: Some believe that undocumented immigrants might compete for jobs with native-born citizens, potentially driving down wages, particularly for low-skilled jobs.

3. Public Resources: Concerns are raised about potential strains on public resources like healthcare, education, and social services.

4. Security Concerns: There are fears that without strict immigration controls, criminals or potential security threats might enter the country.

5. Cultural and Social Concerns: Some individuals believe that a rapid increase in immigration, especially without assimilation, might challenge the cultural or social fabric of the nation.

6. Fairness: There's an argument that individuals waiting in line for legal immigration might view an increase in allowed undocumented immigrants as unfair.

It's crucial to differentiate between the idea of "allowing more undocumented immigrants" and "reforming immigration policies." Some people advocate for comprehensive immigration reform, which might provide pathways to legal status for current undocumented immigrants while enhancing border security and revising future legal immigration channels.

Given the complexity and the various stakeholders involved, any potential solutions often require a multifaceted approach, which takes into consideration the diverse aspects and consequences of immigration policy.