What battle plan does Cassius propose? Why, do you think, does he agree to march to Philippi?
This question refers to the conversation between Brutus and Cassius in Act IV, Scene III. When asked how he feels about marching to Philippi, Cassius bluntly responds, "I do not think it is good." He explains that he feels it would be better to wait for the enemy to come to them, thus wearing themselves out and finding rested men waiting for them upon arrival. Antony would "waste his means, weary his soldiers," while Brutus' men would be "full of rest, defense, and nimbleness."
Brutus accepts that Cassius has "good reasons" but says that these must "give way to better." Cassius does attempt to dissuade him—"Hear me, good brother"—but when Brutus continues in defense of his own proposition, he seems to lose his will to argue. Brutus is evidently dedicated to his own plan; in his speech to Cassius, he uses an extended metaphor to convey the extent of his conviction that "there is a tide in the affairs of men" and that they must "take the current when it serves/Or lose our ventures."
Cassius is loyal to Brutus, ultimately. Earlier in this scene, we get an insight into how their relationship works; Cassius suggests that Brutus knows he is in a unique position which allows him to criticize Cassius:
You know that you are Brutus that speak this,
Or, by the gods, this speech were else your last.
Although Cassius is "an elder soldier," Brutus denies that he is a "better." Brutus is dedicated to his own way of proceeding, and has made clear to Cassius already that he will not be swayed or "budge" to Cassius's will. Meanwhile, Cassius knows that he must stay on the right side of Brutus; he has already pushed things as far as he feels able in the early part of this scene and received nothing but confirmation that arguing with Brutus is futile. As such, he agrees to go to Philippi because arguing any further seems pointless to him.
Cassius, wisely, suggests that they stay at Sardis and rest and recoup while Antony's army uses their time, energy, and supplies to march to Sardis to fight. In addition to being well rested, their armies would occupy the high ground, a huge military advantage in battle.
As far as agreeing with Brutus at this point, probably for the same reason he's agreed throughout the play. Cassius recognizes the importance of Brutus's support and can't do anything to make Brutus upset. If Cassius has any chance to be a leader in a new regime, he will have to be a good buddy of Brutus. That's why Brutus is allowed to make bad decision after bad decision; these conspirators need him and his influence on the commoners just in case they win.