Can visas be stamped in an old passport, provided that I have a new one?

I am a citizen of Ukraine, living in Thailand on a long-term basis.

My current passport is running out of free pages.

I have yet another, older passport which ran out of its period of validity several years ago. We usually need to surrender an old passport, unless it has valid visas, and this is exactly my case (a ten-year visa to a third country, still valid). The old passport has plenty of free pages.

Recently, I was offered a tour to several neighboring countries (namely, Malaysia, Singapore, and Indonesia).

I'm aware I can apply for a new passport in the Embassy of Ukraine in Bangkok, but it takes several weeks to be done, while the tour supposed to occur within two weeks or so.

The question is, may I apply for Malaysian/Singapore/Indonesian visas, providing with both passports and asking to place visas into the old passport? Obviously, I will not be risking to expect for Visa-on-Arrivals, but at least, may I expect to receive normal tourist visas via respective embassies? In other words, would my two passports together comply with the requirement of having available pages?

Update. I greatly appreciate all ideas about possible workarounds, but my question was primarily about interpretation of the requirements: (1) passport¹ within its validity period; and (2) passport² with free pages, whether or not passport¹ and passport² must be the same one. Even if the visas did not take pages at all, there would be also nine entry+exit stamps that use almost 2 remaining pages.