There is no conceivable reason to space out vaccines. An immune system is capable of addressing more than one challenge at a time. During any random day your immune system handles 100's.

Some vaccines are made of inert pieces of the illness producing particles, (viral or bacterial) and generally produce little to no systemic response, ie perceivable reaction.
Other vaccines are of necessity attenuated live viruses. These will produce, more or less, depending the host, a foreshortened, milder illness, to provoke the immune response and provide immunity.

Please note, when an illness is contracted, it is a pitched battle between how fast your immune system can respond versus how fast the invader can reproduce. Vaccines prime your immune system to have already completed the reproduction of necessary immune cells needed for that illness. That is a relatively slow process and it's nice to have that leg up in the fight.