If I double the amount of oxygen molecules, do I double the paramagnetic force? Oxygen is well known to be paramagnetic. 
If I take one molecule, $O_2$, and measure its paramagnetic force due to externally applied magnetic field, and then add another molecule near the first molecule, is the total (paramagnetic) force of the two molecules doubled from having only one molecule?
Or are there forces between the molecules that interact and either reduce or increase the total force at a distance (some type of interference)?
 A: Magnetic forces follow the superposition principle which mandates that the net field at a point due to the field of two or more objects is equal to only the vector sum of the two fields. 
So yes, the force is just doubled, and the force between the molecules don't matter.
Edit after question update: 
Only under the influence of an external field do the dipoles in a paramagnetic bulk align in a particular direction to give a net field. 
So, if you increase the number of molecules without having net increase in the number of dipoles oriented in a particular direction, you'll not record an increase in field. 
A: It is wise to look at what paramagnetism  is

Materials may be classified by their response to externally applied magnetic fields as diamagnetic, paramagnetic, or ferromagnetic. These magnetic responses differ greatly in strength. Diamagnetism is a property of all materials and opposes applied magnetic fields, but is very weak. Paramagnetism, when present, is stronger than diamagnetism and produces magnetization in the direction of the applied field, and proportional to the applied field. Ferromagnetic effects are very large, producing magnetizations sometimes orders of magnitude greater than the applied field and as such are much larger than either diamagnetic or paramagnetic effects. 

Please note: Paramagnetism, when present, is stronger than diamagnetism and produces magnetization in the direction of the applied field, and proportional to the applied field. 

So adding up oxygen atoms without the existence of a magnetic field shows no effect. If a magnetic field is applied  all molecules will show magnetization in the direction of the applied magnetic field.
If only two molecules exist the magnetic dipoles will have random directions and their magnetic fields may either cancel or add up vectorially to some value depended on the distances.
This video may help . The magnet is cooled with liquid nitrogen, and the liquid shows no attraction to the magnet poles. Liquid oxygen is caught by the field within the poles.
Edit after edit.
Paramagnetism (and Magnetism) are not forces per se. They are fields described as the B magnetic field that generate forces on moving charges or on magnetic dipoles, this  last is the paramagnetism .
 

The magnetic moment can be considered to be a vector quantity with direction perpendicular to the current loop in the right-hand-rule direction. The torque is given by



As seen in the geometry of a current loop, this torque tends to line up the magnetic moment with the magnetic field B, so this represents its lowest energy configuration.

The definition of torque is force times lever arm, and that is how one Oxygen molecule will react to the magnetic field.
Two Oxygen molecules will affect each other like two tiny magnets, because of their own magnetic field lines but the field is much weaker than the external B, so it makes no measurable difference to their individual behavior in the presence of an external field.
That is why one separates paramagnetic  from ferromagnetic. In ferromagnetic the fields of the atoms/molecules are strong enough to attract each other and build up larger magnetic domains which are at a stable energetically bound state and a permanent magnet can be formed . In paramagnetic this cannot happen. They can only react to an external stronger field and randomize again. The video with liquid oxygen shows how the oxygen molecules are organized in the direction of the field, attracted to the poles , same as iron filings.
