Yes, it is possible for a second planet to orbit a star without significantly disturbing the orbits of other planets in the same system. In fact, multiple planets can coexist in the same stellar system and maintain stable orbits if certain conditions are met.
The stability of planetary orbits depends on a variety of factors, including the mass, distance, and orbital resonance of the planets. If the planets are sufficiently spaced apart and their orbits are not in resonance (meaning their orbital periods do not have simple integer ratios), they can coexist without significant disruptions.
Additionally, the influence of gravitational forces between planets can be mitigated if the planets are significantly smaller or less massive compared to each other. The mass distribution and distances between the planets play a crucial role in determining the stability of their orbits.
However, it's worth noting that the gravitational interactions among planets can still have some effect on their orbits over long timescales. These effects may lead to slight changes or perturbations in the orbits, but they typically do not result in catastrophic disruptions as long as the system is dynamically stable.
Many multi-planet systems have been discovered in the universe, including our own solar system, which contains multiple planets with stable orbits. The study of planetary dynamics and orbital stability is a complex field, but in general, it is possible for planets to coexist and maintain their orbits without significant disturbances.