New shower venting?

I posted a question about adding a shower a little while ago and appreciated the responses. Well now I am a little farther now I broke up the concrete floor found the cast iron drain pipe but the venting has me puzzled. The sink drain goes straight into the floor under the floor there is a cast iron

90 deg elbow looks like 3" OD this goes to the toilet drain about 2 to 3 feet away then under the toilet it must make a 90 degree turn goes another 2 to 3 feet where it meets the main drain this is also the only vent for the toilet and sink. I was expecting to see something more for venting but the wall behind the sink and toilet is block with no vent lines? Can I just add a "Y" where the sink elbow is and have the shower drain tie in there with no additional venting? the shower drain is about 3 feet away from the sink. Thanks Joe

In a case like this (years ago), the sheer volume of air in the cast iron house drain was relied upon to "kin of" vent the basement fixtures arranged the way yours are.

Today, you wouldn't be allowed to do it and would almost certainly need a vent for the new shower.

Will it work, tying into the sink drain? Maybe. The shower drain will be 2" and you'll need a 2" P-trap under the shower base. Better would be to WYE into the cast iron .

You might give yourself an "out" by TEEing off the shower drain (after the P-trap) with a 1 1/2" line brought up to the surface (by the wall maybe) so you could add a mechanical vent if it were needed.

Presumably this job won't need an inspection...

Jim