Is it more advantageous to summon on a campaign when more Servants are offered?

When there are multiple SSRs or SRs on rate-up at the same time, the chance to get any of them individually is reduced. That's why people recommend solo rate-ups.

You always have only a 1% chance of getting a 5* servant per roll.

If there's a single servant on rate-up, you have a 0.7% chance of getting him (and a 0.3% chance of some random 5*).

If two 5* servants are on rate-up, each of them have a 0.4% chance (and a 0.2% chance of some random 5*).

If three 5* servants are on rate-up, each of them have--IIRC--a 0.3% chance (and a 0.1% chance of some random 5*).

It's never really a good idea to roll when multiples of a rarity are on at the same time unless you're okay with getting any of them. If you're after a specific servant, always go after them if they are the only servant of their rarity on rate-up at that time; ie if you want a 4* only pull for that 4* if there are no other 4*s on rate-up.