You cannot siege with two armies from the same square. You can siege with two or more different armies (from the same city, from another city, from a friend's city, from your nemesis's city) as long as they siege from different squares. A second siege army headed to the same square as the first will either attack the occupying siege (if not NAP'd or confed) or will simply bounce off harmlessly, if the two players are NAP'd or confed.
Sieging with multiple armies will speed up the process somewhat, but also increases the likelihood that one will "overshoot" and reduce the population below the required amount, so it should be used with caution when the intention is to capture the city. If one intends to capture, it is strongly recommended that the siege army from the player who wishes to capture arrive some hours in advance of any other sieges, for reasons described below.
You can reinforce a siege army by sending troops to occupy on the same square. However, the reinforcing troops will not accompany the siege army to storm the city on the raze or capture step -- only those troops actually in the same army as the siege equipment will raze or capture. This can be a problem if there are troops in the target city. In order to deal with this, one can send troops in the siege army -- t2 swords are the best for this purpose, since the raze/capture battle is fought on buildings terrain. One can also send armies separately to raid or attack to reduce or eliminate defending armies. Cavalry armies are often used for this purpose.
When more than one army is sieging, each army will be assigned a population at which the city can be razed or captured. The earliest army to begin bombardment will have the highest population target. All armies that begin bombarding after the first army will have their target population reduced based on the total population of the city when bombardment begins. If a city begins at 10k population, the city must be reduced to 2.5k population in order for the siege army to take the city. If a second army begins to bombard the city after its population has already been reduced to 8k, that army will have the option to raze and capture when the city reaches 2k population.
In any case, the army that is accompanying the siege army will be the army that accompanies the army on the raze/capture step. So if the second army to begin sieging is the only army to have troops available to overcome the troops in the city, one would complete the raze/capture step using the siege page of that army. The population will need to be reduced to the amount based on the total population when that army began bombardment.